math
posted by Lisa on .
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?

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 
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 
thank you both