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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?

  • algebra -

    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.

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