Question

It takes the first pipe 9 more hours to fill the pool than the first and the second pipes together and 7 less hours than it would take the second pipe if it was working alone. How long would it take to fill up the pool if both pipes were working together?

Answer 1

Let the time taken for the first pipe to fill the pool be x hours
time taken for second pipe to fill the pool is (x+7) hours
time taken for both pipes to fill the pull =(x-9) hours
thus fraction of time taken for both will be written as:
1/(x-9)
thus total fraction for pipe 1 and 2 will be
1/x+1/(x+7)=1/(x-9)
solving for x we get:
x=-3 or x=21
but time is positive, then time taken  by first pipe is 21 hours
time taken by both pipes will be 21-9=12 hours