One inlet pipe can fill an empty pool in 6 hours, and a drain can empty the pool in 12 hours. How long will it take the pipe to fill the pool if the drain is left open?

Question

Use t to represent time it takes to fill the pool

Answer 1

t/6 - t/12 = 1

Can you solve for t and answer?

Answer 2

Let x = time it takes to fill the pool if the inlet pipe and drain pipe are both open

1/6 = portion of pool filled per hour by the inlet pipe

1/12 = portion of pool emptied per hour by the drain

1/x = portion of pool filled per hour if the inlet pipe and drain are both open

Then, 1/6 - 1/12 = 1/x

Multiply by the LCD, 12x, to obtain 2x - x = 12

x = 12 hours