An inlet pipe on a swimming pool can be used to fill the pool in 32 hours. The drain pipe can ve used to empty the pool in 34 hours. If the pool is 1/4 filled and then the inket pipe and drain

Question

An inlet pipe on a swimming pool can be used to fill the pool in 32 hours. The drain pipe can ve used to empty the pool in 34 hours. If the pool is 1/4 filled and then the inlet pipe and drain pipe are opened. How many more hours would it take to fill the pool? Round your answer to two decimal places, if needed.

Answer 1

Let x = number of hours to fill the pool.

The inlet pipe fills at an hourly rate of 1/32 of the pool per hour

The drain pipe drains at an hourly rate of 1/34 of the pool per hour.

So the inlet pipe must fill 1/32 times x hours.

The drain pipe must drain out 1/34 times x hours.

So the equation will be

1/32 (x) - 1/34 (x) = 3/4

The minus sign is because the drain pipe is letting water out.

Solve this by multiplying the equation through by the common denominator of 1088.

This gives

34 x - 32 x = 816

2x = 816

x = 408 hours.