Question

One pipe can fill a cistern in 3 hours less than the other. The two pipes together can fill it in 6 hours 40 min. Find the time that each pipe will take to fill the cistern.

Answer 1

Ans: 15 hours and 12 hours

Let the pipes can fill the cistern in x hours and (x−3) hours respectively

Then the part of the tank filled by the pipes in 1 hr are 1x and 1x−3 respectively

Part of the tank filled by both pipes together in 1 hr

=1x+1x−3⋯(1)

Time taken for both the pipes to fill the cistern = 6 hrs and 40 min

=64060=623=203 hour

Therefore, part of the tank filled by both pipes together in 1 hr = 320⋯(2)

From(1) and (2)

1x+1x−3=32020(x−3)+20x=3x(x−3)[∵ Multiplied both sides with 20x(x−3)]40x−60=3x2−9x3x2−49x+60=0x=49±√(−49)2−4×3×606=49±√16816=49±416=15 or 1.33

Cannot take x=1.33 because (x−3) will be negative.

Therefore, x=15

The pipes can fill the cistern in 15 hours and 15 - 3 = 12 hours respectively