Question

A tank has 5 inlet pipes. Three pipes are narrow and two are wide. Each of the three narrow pipes works at 1/2 the rate of each of the wide pipes. All the pipes working together will take what fraction of time taken by the two wide pipes working together to fill the tank?

Answer 1

All pipes working together take 2/7 the time it would take for just the two wide pipes to fill the tank, since their total rate is 7/2 times that of the wide pipes alone.

Step-by-step explanation:

To determine the fraction of time that all the pipes take to fill the tank compared to the two wide pipes working together, it is necessary to compare the rates at which the pipes fill the tank. Let the rate at which each wide pipe fills the tank be represented as '1'. Therefore, the rate of each narrow pipe is '1/2' since it is half the rate of a wide pipe. If we have three narrow pipes, their combined rate is 3*(1/2) = '3/2'. The rate of two wide pipes working together is thus '2'. Summing up all the rates of the pipes gives us 3/2 (narrow pipes) + 2 (wide pipes) = 3/2 + 4/2 = 7/2.

Now, to fill the tank completely using all the pipes, the time taken would be the reciprocal of the total rate, which is 2/7 the time it takes for two wide pipes, which fill at a rate of 2. Consequently, all the pipes working together take 2/7 the time it would take for just the two wide pipes working together to fill the tank.