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Question 1135946: It takes an older pump twice as long to drain a certain pool as it does a newer pump. Working together, it takes the two pumps 2 hours to drain the pool. How long will it take the older pump to drain the pool working alone?
Found 4 solutions by josgarithmetic, Theo, ikleyn, greenestamps:
Answer by josgarithmetic(39620)   (Show Source):
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! let a = the rate of the older pump.
let b = the rate of the newer pump.
general formula is rate * time = quantity of work
quantity of work = 1 drained pool.
older pump takes twice as long to drain the pool than the newer pump.
that means that the rate of the newer pump is 2 times the rate of the older pump.
that gets you b = 2a.
when they work together, their rates are aqditive.
combined rate = a + b
time = 2
quantity of work = 1
formula of rate * time = quantity becomes (a + b) * 2 = 1
since b = 2a, the formula becomes (a + 2a) * 2 = 1
combine like terms to get 3a * 2 = 1
simplify to get 6a = 1
divide both sides by 6 to get a = 1/6
that's the rate of the older pump.
since b = 2a, then b = 2/6.
that's the rate of the newer pump.
formula of (a + b) * 2 = 1 becomes (1/6 + 2/6) * 2 = 1 which becomes 3/6 * 2 = 1 which becomes 1 = 1 which confirms the solution is correct.
rate * time = quantity for the older pump becomes 1/6 * time = 1.
this results in time = 6.
rate * time = quantity for the newer pump becomes 2/6 * time = 1.
this results in time = 3.
your solution is that it will take the older pump 6 hours to drain the pool by itself.
Answer by ikleyn(52799)  (Show Source):
You can put this solution on YOUR website! .
We are given that working together, the two pumps work as effectively as three old pumps, and drain the pool in 2 hours.
Hence, one old pump will drain the pool in 6 hours. ANSWER
Two lines solution, using the POWER of your mind . . .
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
The two-line solution from tutor @ikleyn shows you that logical reasoning can often get you to the solution of a problem much faster, and with far less effort, than a formal algebraic solution.
You should also note that using your brain to do logical reasoning is excellent brain exercise.
So here is another 2-line solution using logical reasoning -- very similar to the one from @ikleyn, yet different.
Since the old pump takes twice as long as the newer one to drain the pool, when working together it only does 1/3 of the job.
So if it can drain 1/3 of the pool in 2 hours, it will take 6 hours for it to drain the whole pool.
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