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How many men to pump the ship dry?
By Isabelle Soh on Friday, September 07, 2001 - 10:17 am:

Hi guys,
I have a question for you to solve.

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?

Please help me and solve this problem.

Thanks,
Isy

By Michael Doré on Friday, September 07, 2001 - 11:38 am:

I think we need more information. At the moment there are three unknowns - the amount of water there to start with, the rate of accumulation of water from the leak and the rate at which each man can pump water out - but only two equations. So we can't solve the problem with the information we have.

By Tom Hardcastle on Friday, September 07, 2001 - 01:06 pm:

You can do it with the given information as follows.
Let the amount of water initially in the boat be m.
Let the rate at which water enters the boat be w.
Let the rate at which one man can pump water out of the boat be d.

Then from the first case
m + 3w + 3×12d = 0
And from the second case
m + 10w + 10×5d = 0

Solving to give w in terms of d gives
w = -2d
Substitution into the original equations gives
m = 15w
To find an answer to the question it is necessary to solve:
m + 2w + 2×n×d = 0
where n is the number of men.
From above, this is
15w + 2w - n×w = 0
Since w is non-zero
n = 17.

Tom.

By Michael Doré on Friday, September 07, 2001 - 02:38 pm:

Ah yes, thanks, I guess I should have actually tried it :-) Of course the reason you can do it is that you don't actually need to determine all the unknowns - in fact you can scale up all the volumes involved by an arbitrary factor without affecting the number of men required.

By Isabelle Soh on Sunday, September 09, 2001 - 06:33 am:

Thanks for the help guys....much appreciated

By David Lee on Friday, September 14, 2001 - 08:32 pm:

Let V be the rate that water leaks
Let W be the rate one man can remove it
Let T be the initial time ellapsed.

(T+3)V = 12x3xW
(T+10)V = 5x10xW

(T+3)/(T+10) = 36/50
T=15

so initial equations become
18V = 36W and 25V = 50W

(T+2)V = ?x2xW
17V = ?(2W)
?= (17/25)/(2/50) = 17