SOLUTION: This is anouther problem that has given me a great deal of trouble. One pipe alone will fill a tank in 7.5 hours. a second pipe will fill it alone in 10 hours. If the second pi

Algebra ->  Rate-of-work-word-problems -> SOLUTION: This is anouther problem that has given me a great deal of trouble. One pipe alone will fill a tank in 7.5 hours. a second pipe will fill it alone in 10 hours. If the second pi      Log On


   

Question 27746: This is anouther problem that has given me a great deal of trouble. One pipe alone will fill a tank in 7.5 hours. a second pipe will fill it alone in 10 hours. If the second pipe were open for 8 hours. And then closed, how long would the frist pipe take to finish filling the tank?
The answer is 1.5 hours, but i don't know how to setup the problem. Thank you.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
One approach to this problem is first find the hourly rate of fill for each pipe. Let's call the first pipe A and the second pipe B.
If pipe A can fill the tank in 7.5 (15/2) hours, then it can fill 2/15 of the tank in 1 hour.
If pipe B can fill the tank in 10 hours, then it can fill 1/10 of the tank in 1 hour.
If pipe B were to be left open for 8 hours, then it would fill 8 X (1/10) of the tank.
So, after 8 hours, 4/5 of the tank would be filled leaving 1/5 of the tank to be filled by pipe A.
Now, pipe A can fill 2/15 of the tank in 1 hour, so how long would it take to fill the 1/5 of the tank?
Divide 1/5 by 2/15 %281%2F5%29%2A%2815%2F2%29+=+3%2F2hours.
Pipe A would need 1.5 hours to finish filling the tank.