A swimming pool can be filled by a pipe in 6 hours and it requires 9 hours to drain it. If the drain was accidentally left open for 6 hours, while the pool was being filled, how long will it take to fill the pool?
In your head:
The LCM of 6 hours and 9 hours is 18 hours. In 18 hours the fill-pipe will
fill the pool 3 times and the drain pipe will have drained it 2 times, so
that's 3-2 = 1 pool filled in 18 hours. Answer: 18 hours.
By algebra.
The fill rate of the fill pipe is 1 pool per 6 hours or 1/6 pool per hour.
The "fill" rate of the drain pipe is the loss of one pool per 9 hours, or the
loss of 1/9 pool per hour, and we indicate a negative rate with a negative
sign, -1/9 pool per hour. The combined fill rate of both pipes is 1 pool per x
hours of 1/x pool per hour. So the equation is gotten by equating the sum of
the fill rates to the combined fill rate:
1/6 - 1/9 = 1/x
Multiply that through by 18x and solve to get 18 hours.
Edwin