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
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.
