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Rational Equations Word-Problems
------=_NextPart_01C9A0BF.8F1C3D00 Content-Location: file:///C:/6457A213/3RationalEquationsWord-Problems_files/slide0005.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Rational Equations Word-Problems
Rational Equations Word-Problems
Rate-of-Work Problems<= /span>
------=_NextPart_01C9A0BF.8F1C3D00 Content-Location: file:///C:/6457A213/3RationalEquationsWord-Problems_files/slide0083.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Rational Equations Word-Problems
Rational Equations Word-Problems
Rate-of-Work Problems
Suppose a job can be completed in x hours, &#= 13;
------=_NextPart_01C9A0BF.8F1C3D00 Content-Location: file:///C:/6457A213/3RationalEquationsWord-Problems_files/slide0084.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Rational Equations Word-Problems
Rational Equations Word-Problems
Rate-of-Work Problems
Suppose a job can be completed in x hours, the rate of the work is define= d to be = 1/x per hr.
------=_NextPart_01C9A0BF.8F1C3D00 Content-Location: file:///C:/6457A213/3RationalEquationsWord-Problems_files/slide0085.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Rational Equations Word-Problems
Rational Equations Word-Problems
Rate-of-Work Problems
Suppose a job can be completed in x hours, the rate of the work is define= d to be = 1/x per hr.
Example:  I can eat a pizza in x hours, fin= d the = rate.
2&fra= c12;        
1/3
2
   Rate per Hour
      x hours
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Rational Equations Word-Problems
Rate-of-Work Problems
Suppose a job can be completed in x hours, the rate of the work is define= d to be = 1/x per hr.
Example:  I can eat a pizza in x hours, fin= d the = rate.
2&fra= c12;        
1/3
1/2
2
   Rate per Hour
      x hours
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Rational Equations Word-Problems
Rate-of-Work Problems
Suppose a job can be completed in x hours, the rate of the work is define= d to be = 1/x per hr.
Example:  I can eat a pizza in x hours, fin= d the = rate.
2&fra= c12;        
3
1/3
1/2
2
   Rate per Hour
      x hours
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Rational Equations Word-Problems
Rate-of-Work Problems
Suppose a job can be completed in x hours, the rate of the work is define= d to be = 1/x per hr.
Example:  I can eat a pizza in x hours, fin= d the = rate.
2/5
2&fra= c12;        
3
1/3
1/2
2
   Rate per Hour
      x hours
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Rational Equations Word-Problems
Similarly, if we know the rate, we can find out the time it takes to finish the job.
------=_NextPart_01C9A0BF.8F1C3D00 Content-Location: file:///C:/6457A213/3RationalEquationsWord-Problems_files/slide0089.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Rational Equations Word-Problems
Rational Equations Word-Problems
Similarly, if we know the rate, we can find out the time it take= s to finish the job.
Example:  How long will it take to do the job with the given rates?
2/3= pizza
6 pizza
¼= pizza
   Rate per Hour
      x hours
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Rational Equations Word-Problems
Similarly, if we know the rate, we can find out the time it take= s to finish the job.
Example:  How long will it take to do the job with the given rates?
2/3= pizza
6 pizza
¼= pizza
4
   Rate per Hour
      x hours
------=_NextPart_01C9A0BF.8F1C3D00 Content-Location: file:///C:/6457A213/3RationalEquationsWord-Problems_files/slide0076_image006.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhoQGDAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAACg AYIAgAAAAAAAAAL/jI+py+0Po5y02ouz3rz7D4biSJbmiabqykrAC8fyTNf2jef6zvf+D+wFgsSi 8YhMKn2IpfMJjUqNw6n1is0em9qu9wuugsfkMpJrTqvXNzH7DS+j4/R61m3P65Xzvf8PhAc4SFjT V4iYKJjI+HfYCKm3GEkJ91iJuTaZyTl22QnqtRlKavVZiho1msqadNoKSxU7u/RKe7uzirtrY8v7 K6MLPOw7DCxszFucvIvMfLv8TOssHRtdDUuNzXq9nartXdodTgpODjp+3mmunpnejskOT/k+Hylv 31ifz4jPj7jvXyF/AgcFLAiIIEI/BxfuUegwT8OIdiBSpDPxYhyL/xrfZOzIhiNINR9HphFpUs6B lPFY0lvp8l5MSCVnirLZDyZOgDsB6uxpECihFkSLGj2KNKnSpROEDnWa8CdUSVMZSq1aByVWJzW3 1vJa8SrYkGMxii17Eq2ls2rJaG0bpCvcQHNJsq3b5S1eHnL35vLr9i5gU4PDCC6sCrGow4q5NtbS 93EwyVgiU36h9zJmxpqLZNZs+fJn0Zw7xzWtqjRqJqufhKY8Grbq1n9p85ltG0dsya9553aF+7ch 4VuCE598nEjvx7uZG0+OGXrc59CbN15+XXogpty7e/8OPrxS7XTJC6Ge3Lpi7OvNnzfgXkj8XOiP q0fMHv98HfkL3/73Xx9x/w3WH4H75VAgYAMqGKBwC/qVIIQH6tbgbw/uFSGGE7ZRYW4X4pUhiBv2 0qFtH9YVIoojGlIibSfOlSKMK9IQI1wv2thiaze2VSOPM87Qo1o7CpnjakOiFSSSPwZTJGpHlpUk lEvGEOVYT1opXpZabslll11OSSWYm8EnJgBXglUlmmWm6dWZbTZpmptbsTnnmnB2JidWdOppJ5li 5lnVnoH2Ceigf94JGqFlmqnomo3++SiYhUIl6FSTOlUppZFOealQmWK66ZKdAvWpp6H+OGpPpZJ6 6oyp7rSqqq2u+CpOscI664i12uRlr77+Cmywwg5LbLHGHgtBAQA7 ------=_NextPart_01C9A0BF.8F1C3D00 Content-Location: file:///C:/6457A213/3RationalEquationsWord-Problems_files/slide0077.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Rational Equations Word-Problems
Rational Equations Word-Problems
Similarly, if we know the rate, we can find out the time it take= s to finish the job.
Example:  How long will it take to do the job with the given rates?
2/3= pizza
 
6 pizza
1/6=
¼= pizza
4
   Rate per Hour
      x hours
------=_NextPart_01C9A0BF.8F1C3D00 Content-Location: file:///C:/6457A213/3RationalEquationsWord-Problems_files/slide0077_image007.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhoQGDAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAACg AYIAgAAAAAAAAAL/jI+py+0Po5y02ouz3rz7D4biSJbmiabqykrAC8fyTNf2jef6zvf+D+wFgsSi 8YhMKn2IpfMJjUqNw6n1is0em9qu9wuugsfkMpJrTqvXNzH7DS+j4/R61m3P65Xzvf8PhAc4SFjT V4iYKJjI+HfYCKm3GEkJ91iJuTaZyTl22QnqtRlKavVZiho1msqadNoKSxU7u/RKe7uzirtrY8v7 K6MLPOw7DCxszFucvIvMfLv8TOssHRtdDUuNzXq9nartXdodTgpODjp+3mmunpnejskOT/k+Hylv 31ifz4jPj7jvXyF/AgcFLAiIIEI/BxfuUegwT8OIdiBSpDPxYhyL/xrfZOzIhiNINR9HphFpUs6B lPFY0lvp8l5MSCVnirLZDyZOgDsB6uxpECihFkSLGj2KNKnSpROEDnWa8CdUSVMZSq1aByVWJzW3 1vJa8SrYkGMxii17Eq2ls2rJaG0bpCvcQHNJsq3b5S1eHnL35vLr9i5gU4PDCC6sCrGow4q5NtbS 93EwyVgiU36h9zJmxpqLZNZs+fJn0Zw7xzWtqjRqJqufhKY8Grbq1n9p85ltG0dsya9553aF+7ch 4VuCE598nEjvx7uZG0+OGXrc59CbN15+XXogpty7e/8OPrxS7XTJC6Ge3Lpi7OvNnzfgXkj8XOiP q0fMHv98HfkL3/73Xx9x/w3WH4H75VAgYAMqGKBwC/qVIIQH6tbgbw/uFSGGE7ZRYW4X4pUhiBv2 0qFtH9YVIoojGlIibSfOlSKMK9IQI1wv2thiaze2VSOPM87Qo1o7CpnjakOiFSSSPwZTJGpHlpUk lEvGEOVYT1opXpZabslll11OSSWYm8EnJgBXglUlmmWm6dWZbTZpmptbsTnnmnB2JidWdOppJ5li 5lnVnoH2Ceigf94JGqFlmqnomo3++SiYhUIl6FSTOlUppZFOealQmWK66ZKdAvWpp6H+OGpPpZJ6 6oyp7rSqqq2u+CpOscI664i12uRlr77+Cmywwg5LbLHGHgtBAQA7 ------=_NextPart_01C9A0BF.8F1C3D00 Content-Location: file:///C:/6457A213/3RationalEquationsWord-Problems_files/slide0078.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Rational Equations Word-Problems
Rational Equations Word-Problems
Similarly, if we know the rate, we can find out the time it take= s to finish the job.
Example:  How long will it take to do the job with the given rates?
2/3= pizza
3/2
6 pizza
1/6=
¼= pizza
4
   Rate per Hour
      x hours
------=_NextPart_01C9A0BF.8F1C3D00 Content-Location: file:///C:/6457A213/3RationalEquationsWord-Problems_files/slide0078_image008.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhoQGDAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAACg AYIAgAAAAAAAAAL/jI+py+0Po5y02ouz3rz7D4biSJbmiabqykrAC8fyTNf2jef6zvf+D+wFgsSi 8YhMKn2IpfMJjUqNw6n1is0em9qu9wuugsfkMpJrTqvXNzH7DS+j4/R61m3P65Xzvf8PhAc4SFjT V4iYKJjI+HfYCKm3GEkJ91iJuTaZyTl22QnqtRlKavVZiho1msqadNoKSxU7u/RKe7uzirtrY8v7 K6MLPOw7DCxszFucvIvMfLv8TOssHRtdDUuNzXq9nartXdodTgpODjp+3mmunpnejskOT/k+Hylv 31ifz4jPj7jvXyF/AgcFLAiIIEI/BxfuUegwT8OIdiBSpDPxYhyL/xrfZOzIhiNINR9HphFpUs6B lPFY0lvp8l5MSCVnirLZDyZOgDsB6uxpECihFkSLGj2KNKnSpROEDnWa8CdUSVMZSq1aByVWJzW3 1vJa8SrYkGMxii17Eq2ls2rJaG0bpCvcQHNJsq3b5S1eHnL35vLr9i5gU4PDCC6sCrGow4q5NtbS 93EwyVgiU36h9zJmxpqLZNZs+fJn0Zw7xzWtqjRqJqufhKY8Grbq1n9p85ltG0dsya9553aF+7ch 4VuCE598nEjvx7uZG0+OGXrc59CbN15+XXogpty7e/8OPrxS7XTJC6Ge3Lpi7OvNnzfgXkj8XOiP q0fMHv98HfkL3/73Xx9x/w3WH4H75VAgYAMqGKBwC/qVIIQH6tbgbw/uFSGGE7ZRYW4X4pUhiBv2 0qFtH9YVIoojGlIibSfOlSKMK9IQI1wv2thiaze2VSOPM87Qo1o7CpnjakOiFSSSPwZTJGpHlpUk lEvGEOVYT1opXpZabslll11OSSWYm8EnJgBXglUlmmWm6dWZbTZpmptbsTnnmnB2JidWdOppJ5li 5lnVnoH2Ceigf94JGqFlmqnomo3++SiYhUIl6FSTOlUppZFOealQmWK66ZKdAvWpp6H+OGpPpZJ6 6oyp7rSqqq2u+CpOscI664i12uRlr77+Cmywwg5LbLHGHgtBAQA7 ------=_NextPart_01C9A0BF.8F1C3D00 Content-Location: file:///C:/6457A213/3RationalEquationsWord-Problems_files/slide0009.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Rational Equations Word-Problems
Rational Equations Word-Problems
Rate-of-Work Problems
When solving work-proble= ms, rates may be added.
------=_NextPart_01C9A0BF.8F1C3D00 Content-Location: file:///C:/6457A213/3RationalEquationsWord-Problems_files/slide0090.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Rational Equations Word-Problems
Rational Equations Word-Problems
Rate-of-Work Problems
When solving work-proble= ms, rates may be added (not the hours it takes to complete the = job).
------=_NextPart_01C9A0BF.8F1C3D00 Content-Location: file:///C:/6457A213/3RationalEquationsWord-Problems_files/slide0010.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Rational Equations Word-Problems
Rational Equations Word-Problems
Rate-of-Work Problems
When solving work-proble= ms, rates may be added (not the hours it takes to complete the = job). =
Example: I can eat a pizza in 2 hours, Mary can eat one in 3 hours. Find the combined rate.
------=_NextPart_01C9A0BF.8F1C3D00 Content-Location: file:///C:/6457A213/3RationalEquationsWord-Problems_files/slide0080.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Rational Equations Word-Problems
Rational Equations Word-Problems
Rate-of-Work Problems
When solving work-proble= ms, rates may be added (not the hours it takes to complete the = job). =
Example: I can eat a pizza in 2 hours, Mary can eat one in 3 hours. Find the combined rate.
Mary
I
1/3
3
1/2
2
Rate per Hour<= /span>
      x hours
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Rational Equations Word-Problems
Rate-of-Work Problems
When solving work-proble= ms, rates may be added (not the hours it takes to complete the = job). =
Example: I can eat a pizza in 2 hours, Mary can eat one in 3 hours. Find the combined rate.
Mary
I
1/3
3
1/2
2
Rate per Hour<= /span>
      x hours
Hence the comb= ined rate is 1/2 + 1/3
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Rational Equations Word-Problems
Rate-of-Work Problems
When solving work-proble= ms, rates may be added (not the hours it takes to complete the = job). =
Example: I can eat a pizza in 2 hours, Mary can eat one in 3 hours. Find the combined rate.
Mary
I
1/3
3
1/2
2
Rate per Hour<= /span>
      x hours
Hence the comb= ined rate is 1/2 + 1/3 =3D 5/6 per hr.
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Rational Equations Word-Problems
Example: I can eat a pizza in 2 hours. Mary = 3;
can e= at one in 3 hours. How long will it take if
we bo= th eat the same pizza?
 
------=_NextPart_01C9A0BF.8F1C3D00 Content-Location: file:///C:/6457A213/3RationalEquationsWord-Problems_files/slide0012.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Rational Equations Word-Problems
Rational Equations Word-Problems
Example: I can eat a pizza in 2 hours. Mary = 3;
can e= at one in 3 hours. How long will it take if
we bo= th eat the same pizza?
From = last question. The combined rate is
5/6 (= pizza) per hr. 
  
------=_NextPart_01C9A0BF.8F1C3D00 Content-Location: file:///C:/6457A213/3RationalEquationsWord-Problems_files/slide0091.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Rational Equations Word-Problems
Rational Equations Word-Problems
Example: I can eat a pizza in 2 hours. Mary = 3;
can e= at one in 3 hours. How long will it take if
we bo= th eat the same pizza?
From = last question. The combined rate is
5/6 (= pizza) per hr. 
Hence= , it will take 6/5 hr.  if both of us eat= the
same pizza.  
------=_NextPart_01C9A0BF.8F1C3D00 Content-Location: file:///C:/6457A213/3RationalEquationsWord-Problems_files/slide0013.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Rational Equations Word-Problems
Rational Equations Word-Problems
Example: A pipe can fill a pool in 3 hours. A &= #13;
secon= d pipe can fill it in 4 hours. How long will
It ta= ke if both pipes are used?
------=_NextPart_01C9A0BF.8F1C3D00 Content-Location: file:///C:/6457A213/3RationalEquationsWord-Problems_files/slide0093.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Rational Equations Word-Problems
Rational Equations Word-Problems
Example: A pipe can fill a pool in 3 hours. A &= #13;
secon= d pipe can fill it in 4 hours. How long will
It ta= ke if both pipes are used?
combi= ned
2nd pipe
1st pipe
   Rate per Hour
     hours
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Rational Equations Word-Problems
Example: A pipe can fill a pool in 3 hours. A &= #13;
secon= d pipe can fill it in 4 hours. How long will
It ta= ke if both pipes are used?
combi= ned
2nd pipe
1st pipe
x
4
3
   Rate per Hour
      hours
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Rational Equations Word-Problems
Example: A pipe can fill a pool in 3 hours. A &= #13;
secon= d pipe can fill it in 4 hours. How long will
It ta= ke if both pipes are used?
combi= ned
2nd pipe
1st pipe
1/x
x
1/4
4
1/3
3
   Rate per Hour
      x hours
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Rational Equations Word-Problems
Example: A pipe can fill a pool in 3 hours. A &= #13;
secon= d pipe can fill it in 4 hours. How long will
It ta= ke if both pipes are used?
combi= ned
2nd pipe
1st pipe
1/x
x
1/4
4
1/3
3
   Rate per Hour
      x hours
Rates can be added:     
1
3
1
4
+
=3D
1
x
------=_NextPart_01C9A0BF.8F1C3D00 Content-Location: file:///C:/6457A213/3RationalEquationsWord-Problems_files/slide0096_image015.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlh5AGDAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAADj AYIAgAAAAAAAAAL/jI+py+0Po5y02ouz3rz7D4biSJbmiabqyrbuqwHyTNf2jef6zvf+D8wFgsSi 8YhM2obKpvMJjToR0qr1WmRit9yuTOsNi8dNKvmM/oHT7DZt7Y7Lsea5XQy/66/5vf+/Uwc4WEZo WHiYSCio2MjT5xhZAylZiXdgmfmmyQlA2Qn6xBiq+EkKaHqqGjS6OpjqagcbS3vTWqs3i8umu1t7 6yvXGzw2TKwKfMyrvGfMDJr8TOYsbUVdbRmN7XW9LeodrA1ON75c/ot5Pq1+1s3+mv7OLY9Hjxxv T57P5b4vi+9PSr+AQghyEmeQyMCEkxhmA+gwycKInihGQmgxUEZE/xsPYexoCySSiSL5QCzZg6RD lSijfGxZESYQljLLnKwZEmdKnXdetqRpECjPLDeHfjGqQyhSNUWNKvX3dOmjpkOj5rMqVQhVnljp dc26ZKvOr+/Igp3hE6VZdWvPpi3ZtlzcrG9FzgV3d2ldkHm39XUKI7DgwYQLGz6MOPFfaYsZn0Wz t2PjZ5NxRt5YWVlmmZczbib2+adYy4/Rlp42umZoX6vhpuZ8OmZsbq9htsZ1m2/tn7FzS96ttvfs MJ0t+o513DNwuMKHdylOMfkq6dGX223ufAv0iNRPdV9pnS/27CYNnP4eCn3C7SvHk6/CnqH6TvMJ xl/v/r3L8JLz6/8XxR9m/v1nk3ml1acJglAF6NmABErEoHEOPnjEfUFNSCFRBj6mYDYZQmGhfRh+ OFOE0Y1Iog+Krchiiy6+CGOMH5yHYopTbehWjTYmZSJ3Ou6IQ4gBdVgJkfYICdWPQIaFI1hGXrRk hT22R2OUGj7ZCJZZWnlllQdyqdCU8ikJJpL7aFkKmKyIiZ+XaqbE5oVuvhlInCLOSadWTdJFJpdm XtWnlX8eGWiUg3pV6JKHyoNmIo2es2hZiQIZKTuPGnLpOJWyNemOm0LaqY2fyhVqiqNqWiqJp+KV 6oerepPpK3nCuadUsaIy6423+rErr7nWKWOwwg5LbLHGioAnn7+z6tlrLq1m+Kpfz1IYLTbNOrts kHYOOe2D1VZzbU/ZalurXt0S+K1jyY6bLmXn/tcuM+HKMq4t2ya5brbxavaufvseM+8cAQN875n9 vvcvaAeTl3A4C2fXMGsPOxfxLgPHcXE4BQOa77IV4zbxcB//EvJsI9OScRspW7wxoR3/ejJyJffW MqIv5xqzKyunsTM65SLVczv1Mhl0MTOfVzOjRx94bNNOPw111FJPTXXVVl8NdQEAOw== ------=_NextPart_01C9A0BF.8F1C3D00 Content-Location: file:///C:/6457A213/3RationalEquationsWord-Problems_files/slide0097.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Rational Equations Word-Problems
Rational Equations Word-Problems
Example: A pipe can fill a pool in 3 hours. A &= #13;
secon= d pipe can fill it in 4 hours. How long will
It ta= ke if both pipes are used?
combi= ned
2nd pipe
1st pipe
1/x
x
1/4
4
1/3
3
   Rate per Hour
      x hours
Rates can be added:
Clear denom with 12x:     
1
3
1
4
+
=3D
1
x
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Rational Equations Word-Problems
Example: A pipe can fill a pool in 3 hours. A &= #13;
secon= d pipe can fill it in 4 hours. How long will
It ta= ke if both pipes are used?
combi= ned
2nd pipe
1st pipe
1/x
x
1/4
4
1/3
3
   Rate per Hour
      x hours
Rates can be added:
Clear denom with 12x:     
1
3
1
4
+
=3D
1
x
[
]*12x
------=_NextPart_01C9A0BF.8F1C3D00 Content-Location: file:///C:/6457A213/3RationalEquationsWord-Problems_files/slide0098_image017.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlh5AGDAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAADj AYIAgAAAAAAAAAL/jI+py+0Po5y02ouz3rz7D4biSJbmiabqyrbuqwHyTNf2jef6zvf+D8wFgsSi 8YhM2obKpvMJjToR0qr1WmRit9yuTOsNi8dNKvmM/oHT7DZt7Y7Lsea5XQy/66/5vf+/Uwc4WEZo WHiYSCio2MjT5xhZAylZiXdgmfmmyQlA2Qn6xBiq+EkKaHqqGjS6OpjqagcbS3vTWqs3i8umu1t7 6yvXGzw2TKwKfMyrvGfMDJr8TOYsbUVdbRmN7XW9LeodrA1ON75c/ot5Pq1+1s3+mv7OLY9Hjxxv T57P5b4vi+9PSr+AQghyEmeQyMCEkxhmA+gwycKInihGQmgxUEZE/xsPYexoCySSiSL5QCzZg6RD lSijfGxZESYQljLLnKwZEmdKnXdetqRpECjPLDeHfjGqQyhSNUWNKvX3dOmjpkOj5rMqVQhVnljp dc26ZKvOr+/Igp3hE6VZdWvPpi3ZtlzcrG9FzgV3d2ldkHm39XUKI7DgwYQLGz6MOPFfaYsZn0Wz t2PjZ5NxRt5YWVlmmZczbib2+adYy4/Rlp42umZoX6vhpuZ8OmZsbq9htsZ1m2/tn7FzS96ttvfs MJ0t+o513DNwuMKHdylOMfkq6dGX223ufAv0iNRPdV9pnS/27CYNnP4eCn3C7SvHk6/CnqH6TvMJ xl/v/r3L8JLz6/8XxR9m/v1nk3ml1acJglAF6NmABErEoHEOPnjEfUFNSCFRBj6mYDYZQmGhfRh+ OFOE0Y1Iog+Krchiiy6+CGOMH5yHYopTbehWjTYmZSJ3Ou6IQ4gBdVgJkfYICdWPQIaFI1hGXrRk hT22R2OUGj7ZCJZZWnlllQdyqdCU8ikJJpL7aFkKmKyIiZ+XaqbE5oVuvhlInCLOSadWTdJFJpdm XtWnlX8eGWiUg3pV6JKHyoNmIo2es2hZiQIZKTuPGnLpOJWyNemOm0LaqY2fyhVqiqNqWiqJp+KV 6oerepPpK3nCuadUsaIy6423+rErr7nWKWOwwg5LbLHGioAnn7+z6tlrLq1m+Kpfz1IYLTbNOrts kHYOOe2D1VZzbU/ZalurXt0S+K1jyY6bLmXn/tcuM+HKMq4t2ya5brbxavaufvseM+8cAQN875n9 vvcvaAeTl3A4C2fXMGsPOxfxLgPHcXE4BQOa77IV4zbxcB//EvJsI9OScRspW7wxoR3/ejJyJffW MqIv5xqzKyunsTM65SLVczv1Mhl0MTOfVzOjRx94bNNOPw111FJPTXXVVl8NdQEAOw== ------=_NextPart_01C9A0BF.8F1C3D00 Content-Location: file:///C:/6457A213/3RationalEquationsWord-Problems_files/slide0099.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Rational Equations Word-Problems
Rational Equations Word-Problems
Example: A pipe can fill a pool in 3 hours. A &= #13;
secon= d pipe can fill it in 4 hours. How long will
It ta= ke if both pipes are used?
combi= ned
2nd pipe
1st pipe
1/x
x
1/4
4
1/3
3
   Rate per Hour
      x hours
Rates can be added:
Clear denom with 12x:     
1
3
1
4
+
=3D
1
x
[
]*12x
4x
------=_NextPart_01C9A0BF.8F1C3D00 Content-Location: file:///C:/6457A213/3RationalEquationsWord-Problems_files/slide0099_image018.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlh5AGDAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAADj AYIAgAAAAAAAAAL/jI+py+0Po5y02ouz3rz7D4biSJbmiabqyrbuqwHyTNf2jef6zvf+D8wFgsSi 8YhM2obKpvMJjToR0qr1WmRit9yuTOsNi8dNKvmM/oHT7DZt7Y7Lsea5XQy/66/5vf+/Uwc4WEZo WHiYSCio2MjT5xhZAylZiXdgmfmmyQlA2Qn6xBiq+EkKaHqqGjS6OpjqagcbS3vTWqs3i8umu1t7 6yvXGzw2TKwKfMyrvGfMDJr8TOYsbUVdbRmN7XW9LeodrA1ON75c/ot5Pq1+1s3+mv7OLY9Hjxxv T57P5b4vi+9PSr+AQghyEmeQyMCEkxhmA+gwycKInihGQmgxUEZE/xsPYexoCySSiSL5QCzZg6RD lSijfGxZESYQljLLnKwZEmdKnXdetqRpECjPLDeHfjGqQyhSNUWNKvX3dOmjpkOj5rMqVQhVnljp dc26ZKvOr+/Igp3hE6VZdWvPpi3ZtlzcrG9FzgV3d2ldkHm39XUKI7DgwYQLGz6MOPFfaYsZn0Wz t2PjZ5NxRt5YWVlmmZczbib2+adYy4/Rlp42umZoX6vhpuZ8OmZsbq9htsZ1m2/tn7FzS96ttvfs MJ0t+o513DNwuMKHdylOMfkq6dGX223ufAv0iNRPdV9pnS/27CYNnP4eCn3C7SvHk6/CnqH6TvMJ xl/v/r3L8JLz6/8XxR9m/v1nk3ml1acJglAF6NmABErEoHEOPnjEfUFNSCFRBj6mYDYZQmGhfRh+ OFOE0Y1Iog+Krchiiy6+CGOMH5yHYopTbehWjTYmZSJ3Ou6IQ4gBdVgJkfYICdWPQIaFI1hGXrRk hT22R2OUGj7ZCJZZWnlllQdyqdCU8ikJJpL7aFkKmKyIiZ+XaqbE5oVuvhlInCLOSadWTdJFJpdm XtWnlX8eGWiUg3pV6JKHyoNmIo2es2hZiQIZKTuPGnLpOJWyNemOm0LaqY2fyhVqiqNqWiqJp+KV 6oerepPpK3nCuadUsaIy6423+rErr7nWKWOwwg5LbLHGioAnn7+z6tlrLq1m+Kpfz1IYLTbNOrts kHYOOe2D1VZzbU/ZalurXt0S+K1jyY6bLmXn/tcuM+HKMq4t2ya5brbxavaufvseM+8cAQN875n9 vvcvaAeTl3A4C2fXMGsPOxfxLgPHcXE4BQOa77IV4zbxcB//EvJsI9OScRspW7wxoR3/ejJyJffW MqIv5xqzKyunsTM65SLVczv1Mhl0MTOfVzOjRx94bNNOPw111FJPTXXVVl8NdQEAOw== ------=_NextPart_01C9A0BF.8F1C3D00 Content-Location: file:///C:/6457A213/3RationalEquationsWord-Problems_files/slide0100.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Rational Equations Word-Problems
Rational Equations Word-Problems
Example: A pipe can fill a pool in 3 hours. A &= #13;
secon= d pipe can fill it in 4 hours. How long will
It ta= ke if both pipes are used?
combi= ned
2nd pipe
1st pipe
1/x
x
1/4
4
1/3
3
   Rate per Hour
      x hours
Rates can be added:
Clear denom with 12x:     
1
3
1
4
+
=3D
1
x
[
]*12x
4x
3x
12
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Rational Equations Word-Problems
Example: A pipe can fill a pool in 3 hours. A &= #13;
secon= d pipe can fill it in 4 hours. How long will
It ta= ke if both pipes are used?
combi= ned
2nd pipe
1st pipe
1/x
x
1/4
4