# math

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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?

• math -

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

• math -

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

• math -

thank you both

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