posted by Saige on .
Pump A can fill a swimming pool in 6 hours and pump B can fill the same pool in 4 hours. The two pumps began working together to fill an empty pool, but after 40 minutes pump B broke down, and pump A had to complete the job alone. The pool was scheduled to open 4 hours after the pumping started. Was it full by then, or did the opening have to be delayed?
rewording to indicate the rate of completion,
a = 1/6 pool/hr
b = 1/4 pool/hr
they work together for 2/3 hour, so they filled
(1/6 + 1/4)*2/3 = 5/18 pool
So, how long does it take A to fill the other 13/18 pool?
13/18 / 1/6 = 13/3 hour
So, the whole pool took 2/3 + 13/3 = 15/3 = 5 hours to fill, finishing an hour late.