If it takes 4 identical pipes 2 hours to fill a pool, how many hours will it take 1 pipe alone to fill the same pool?

F) 16 hrs

G) 10hrs

H) 8 hrs

J) 4 hrs

K) none of these

Hi!

This is an example of inverse variation, the equation being xy = k, with k being a constant. Inverse variation is essentially when one variable goes up, the other goes down so when they're multiplied, they always get a constant, or k.

x and y, in this case, would be the number of pipes, and the number of hours taken. I'm just going to assign x to the number of pipes and y the hours taken.

So if you look at the 4 identical pipes taking 2 hours, you can assign 4 to x and 2 to y. 4 * 2 = 8, meaning k = 8.

Now, to find how many hours it will take one pipe to fill the same pool, assign x = 1, and then solve for y.

Now just take x = 1 and k = 8, fill it in, and solve.

1y = 8

y = 8

So the answer is 8 hours, or H.

Suppose one pipe alone can fill it in x hour

one hour work of one pipe = 1/x work

one hour work of 4 pipes together = 4/x work

2 hour work of four pipes = 2 * (4/x) = 8/x work

but all four together in 2 hours did complete work that is 1

so 8/x = 1

hence x = 8

so one pipe alone can fill it in 8 hours

Answer : 8