Question

two pipescan fill a swimming pool in 12 hrs. if the pipe of larger diameter is used for 4 hrs and the pipe of smaller diameter for 9 hrs, only the half the pool can be filled. how long would it take for each pipe to fill the pool seperately

Answer 1

Let larger pipe rate be x hrs/job
Let smaller pipe rate be y hrs/job
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Equations:
x + y = 1/12
4x+9y = 1/2
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Modify to get:
24x + 24y = 2
24x + 54y = 3
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Subtract and solve for "y":
30y = 1
y = 1/30 job/hr (rate of the smaller diameter pipe)
Smaller pipe would take 30 hrs to fill the pool.
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Solve for "x"
x + (1/30) = 1/12
x = (1/12)-(1/30)
x = (18/(12*30)) = 1/20 job/hr
Larger pipe would take 20 hrs to fill the pool.