math

One pump can empty a pool in 5 days, whereas a second pump can empty the pool in 7 days. How long will it take the two pumps, working together, to empty the pool?

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  1. Pump 1 does (1/5) pool/day
    pump 2 does (1/7) pool/day
    together they do (1/5)+(1/7) pool/day
    that is
    7/35 + 5/35 = 12/35 pool/day

    so it will take 35/12 = 2.92 days/pool

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  2. rate of 1st pump = pool/5
    rate of 2nd pump = poo/7
    combined rate = pool/5 + pool/7 = (12/35)pool

    time at combined rate = pool / ((12/35)pool) = 35/12 or 2.916667

    it will take about 2.92 hours or 2hrs, 55 minutes

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  3. thank you both

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