a large pump can empty a swimming pool in 100 hours, whereas a small pump can empty the pool in 160 hours. How long will it take to empty the pool if both pumps are used?

Question

a large pump can empty a swimming pool in 100 hours, whereas a small pump can empty the pool in 160 hours.  How long will it take to empty the pool if both pumps are used?

anonymous · Answer

do u have the answer? I found ~61.54hrs. If that's right then I think I can tell u how.

anonymous · Answer

I can't figure it out at all.  I've been stuck on this one for a while :(

anonymous · Answer

but do you have the numerical answer? Because if my answer's wrong so there's no point to show the method

anonymous · Answer

it says 62

anonymous · Answer

ok, so let's call the tank capacity V (litres), flow rate through large pump F1 and through small pump F2. t1= 100, t2= 160
For pump 1, flow rate F1=V/t1=V/100 (litres/hr)
For pump 2, flow rate F2=V/t2=V/160 (litres/hr)

when 2 pumps run at the same time, we have total flow rate, say F, equal to F1+F2
so F=F1+F2=V/100+V/160=(13V)/800

so the time needed is t = V/F = V/ ((13V)/800)=800/13~61.54~62hrs
hope that clear enough :)

anonymous · Answer

Thanks! just one question: how did u get the 13?

anonymous · Answer

calculator? lol
1/100+1/160= 8/800+5/800 =13/800

anonymous · Answer

oh I understand now. Thanks so much for your help. You're a lifesaver!

anonymous · Answer

ur welcome