Leaky Ship

Date: 08/30/97 at 00:50:08
From: windows
Subject: Leaky Ship

A ship has sprung a leak. Water is coming in at a uniform rate and 
some has already accumulated when the leak is detected. At this point 
12 men of equal skill can pump the ship dry in 3 hours, while 5 men 
require 10 hours. How many men are needed to pump it dry in 2 hours?

Date: 09/03/97 at 10:47:03
From: Doctor Rob
Subject: Re: Leaky Ship

Let the amount of water in the ship be W. Let the rate of leakage be 
R gallons per hour. Then the amount of water which has to be pumped 
out after H hours is W + R*H. Let the amount of water one man can pump 
in 1 hour be M. Then 3*12*M = W + 3*R, and 5*10*M = W + 10*R.  
Eliminating W, we find that R = 2*M. Substituting, we find W = 30*M.  

Let x be the number of men required. Then x*2*M = W + 2*R, which you 
can solve for x.

-Doctor Rob,  The Math Forum
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