SOLUTION: Two pumps of different sizes, working together, can empty a fuel tank in 5 hours. The larger pump can empty this tank in 4 hours less time than the smaller. If the larger pump is o

Question 157698: Two pumps of different sizes, working together, can empty a fuel tank in 5 hours. The larger pump can empty this tank in 4 hours less time than the smaller. If the larger pump is out of order, how long will it take the smaller one to do the job alone?
Answer by gonzo(654) (Show Source): You can put this solution on YOUR website!
not terribly sure because ran out of time but i think this is the answer.
let p1 = rate of the larger pump.
let p2 = rate of the smaller pump.
both pumps working for 5 hours can drain the tank.
so 5*p1 + 5*p2 = x where x is the amount of fuel in the tank.
which means p1 is pumping for 5 hours and p2 is pumping for 5 hours.
problem states that pump 1 can drain the tank by itself in 4 hours less than pump 2 can drain the tank by itself.
so p1 * (t-4) = x
and p2 * (t) = x
if they both work by themselves than they both can drain 2 * the tank.
so p1 * (t-4) + p2 * (t) = 2x = 10*p1 + 10*p2 since in 10 hours they can both drain the tank twice working together.
so, .....
p1 * (t-4) = 10 * p1
and p2 * (t) = 10 * p2
solving for p1 we get
p1 * t - 4 * p1 = 10 * p1
which becomes
p1 * t = 6 * p1
which becomes
t = 6
it takes p1 6 hours to drain the tank.
solving for p2 we get
p2 * t = 10 * p2
which becomes
t = 10
it takes p2 10 hours to drain the tank.
answer is it takes p2 10 hours to drain the tank.
p1 takes 6 hours which is 4 hours less so the equation looks sound.

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