Question

One pipe can fill a pool 1.5 times faster than a second pipe. If both pipes are open, the pool can be filled in 6 hours. If only the slower pipe is open, how long would it take to fill the pool?

a) 9 hours
b) 10 hours
c) 12 hours
d) 15 hours

Answer 1

By setting up an algebraic equation based on the given filling rates, we deduce that the slower pipe takes 15 hours to independently fill the pool.

Step-by-step explanation:

The student's question relates to the rate at which two pipes can fill a pool and is solved using algebraic methods to find the time it takes for the slower pipe to fill the pool on its own. Let's denote the filling rate of the faster pipe as 1.5x and the rate of the slower pipe as x. If both pipes working together fill the pool in 6 hours, the combined rate is 1/6 pools per hour. Therefore, we have the equation:

\(1.5x + x = 1/6\)

Solving this equation for x, we find:

\(2.5x = 1/6\)

\(x = 1/15\)

This means the slower pipe has a rate of 1/15th of the pool per hour. To find out how long it takes for the slower pipe to fill the pool, we take the reciprocal of the rate:

\(Time = 1/x = 15\ hours\)

Therefore, the slower pipe takes 15 hours to fill the pool on its own, which corresponds to choice (d).