7 men can survive on 13 quarts of water or 2 weeks. How many quarts are needed by 21 men to survive 4 weeks?

A) 78

B) 52

C) 39

D) 26

E) 13

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- Jul 8th 2013, 11:01 AMusre1237 men survive on 13 quarts
7 men can survive on 13 quarts of water or 2 weeks. How many quarts are needed by 21 men to survive 4 weeks?

A) 78

B) 52

C) 39

D) 26

E) 13 - Jul 8th 2013, 01:01 PMebainesRe: 7 men survive on 13 quarts
You've been given a rate for water consumption by 7 men over 2 weeks. If there are now three times as many men, and they need water for twice as long, you can see that it will require 6 times as much water, right?

More formally - the rate of consumption of water per man-week is 13 Qt per 2 weeks per 7 men, or: $\displaystyle \frac {13\ Qt}{(2\ wk \times 7\ men)} = \frac { 13}{14} \frac {Qt}{man-week}$. Given 4 weeks and 21 men, the amount of water needed is:

$\displaystyle \frac {13}{14} \frac {Qt}{man-wk} \times 4\ wks \times 21\ men $ - Jul 8th 2013, 01:04 PMHallsofIvyRe: 7 men survive on 13 quarts
Is your question "How can I instantly know the answer without doing

**any**calculations at all"? Is so, I can't help you!

But it seems to me that you want to you want to start by calculating "quarts per man per week". And "per" typically means "divide" as in "if you drive 400 miles in 5 hours you are driving at 400 mi/5 hr= 400/5 mi/hr= 80 miles**per**hour. - Jul 8th 2013, 01:07 PMemakarovRe: 7 men survive on 13 quarts
Already typed this before I saw post #2.

Request the largest supply; you won't go wrong. (Smile)

The key is to compute in terms of men-weeks (men times weeks). For example, the following amounts of water are all the same: water needed for 2 men and 6 weeks, for 3 men and 4 weeks, 4 men and 3 weeks, and 12 men and 1 week. All these amounts equal what 1 man needs for 1 week times 12. So, find how many quarts make up one man-week and then find how many men-weeks are required by the question. - Jul 8th 2013, 05:42 PMSorobanRe: 7 men survive on 13 quarts
Hello, usre123!

You can "talk" your way through this problem.

Quote:

7 men can survive on 13 quarts of water for 2 weeks.

How many quarts are needed by 21 men to survive 4 weeks?

. . (A) 78 . . (B) 52 . . (C) 39 . . (D) 26 . . (E) 13

We have:

. . $\displaystyle \begin{array}{|c|c|c|} \hline \text{Men} & \text{Water} & \text{Weeks} \\ \hline 7 & 13 & 2 \\ \hline \end{array}$

If we triple the number of men, three times the amount of water is needed.

. . $\displaystyle \begin{array}{|c|c|c|} \hline \text{Men} & \text{Water} & \text{Weeks} \\ \hline {\color{blue}21} & {\color{red}39} & 2 \\ \hline \end{array}$

If we double the number of weeks, twice the amount of water is needed.

. . $\displaystyle \begin{array}{|c|c|c|} \hline \text{Men} & \text{Water} & \text{Weeks} \\ \hline 21 & {\color{red}78} & {\color{blue}4} \\ \hline \end{array}$

Answer:-$\displaystyle (A)\;78$

- Jul 8th 2013, 05:50 PMusre123Re: 7 men survive on 13 quarts
^ thank you Soroban. unfortunately, the answer is 26. And Emakarov and HallsofIvy, I tried to do it for about 30 minutes myself. I just didn't know I needed to post my solutions here as well. Next time I'll be sure to do so. I thought it would be no good, since I'm not getting the right answer.

What i had done: water per man per week is 6.5/7. So multiply that by 4*21, doesn't give me an answer. - Jul 8th 2013, 06:26 PMShadowKnight8702Re: 7 men survive on 13 quarts
Sorobsn is absolutely correct, the answer is 78. Either you phrased the question incorrectly or the answer itself is wrong. 21 men is 3 x 7, so that means in two weeks, you need three times more quarts, so that means 13 * 3, which is 39. Now since this is for 4 weeks, not 2, that means we have to double the 39 and we get 78. 26 is most definitely not the answer.

- Jul 8th 2013, 07:29 PMusre123Re: 7 men survive on 13 quarts
Allright I'll ask the teacher today. thanks guys. I'll get back to you once I have him solve it.

- Jul 8th 2013, 08:34 PMibduttRe: 7 men survive on 13 quarts
Once again a question based on unitary method.

as a matter of principal what we want to find should be kept on the end. thus we have:

7 men can survive for 2 weeks on = 13 quarts of water

1 men can survive for 2 weeks on = 13/7 quarts of water [ One man will require less water ]

1 men can survive for 1 weeks on = 13/(7*2) quarts of water [ One man will require less water for 1 week than for 2 weeks]

21 men can survive for 1 weeks on = ( 13* 21 )/(7*2) quarts of water [21 men will require more water for 1 week than 1 man]

8 men can survive for 4 weeks on = ( 13* 21 *4 )/(7*2) quarts of water [21 men will require more water for 4 week than 1 week]

Now one can simplify and get the correct answer. A is the correct answer - Jul 9th 2013, 05:43 AMHallsofIvyRe: 7 men survive on 13 quarts
I and the others gave a way of solving general problems like this. However, the number given in

**this**problem make it very simple.

we are told that 7 men require 13 quarts of water for 2 weeks. We are asked about the water required by 21 men for 4 weeks.

We can argue that the are 21/7= 3 times as many men now so they will require three times as much water, 3(13)= 39 quarts just for the same two weeks. And they need the water for 4/2= 2 times as many weeks so need 2(39)= 78 quarts of water.