Problem Solving

M7MBA wrote:Carl can wash all the windows of his house in 6 hours. His wife Maggie can wash all the windows in 4 hours. How many hours will it take for both of them working together to wash all the windows?

A. 2
B. 2 1/4
C. 2 2/5
D. 4 1/2
E. 5

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For work questions, there are two useful rules:

Rule #1: If a person can complete an entire job in k hours, then in one hour, the person can complete 1/k of the job
Example: If it takes Sue 5 hours to complete a job, then in one hour, she can complete 1/5 of the job. In other words, her work rate is 1/5 of the job per hour

Rule #2: If a person completes a/b of the job in one hour, then it will take b/a hours to complete the entire job
Example: If Sam can complete 1/8 of the job in one hour, then it will take him 8/1 hours to complete the job.
Likewise, if Joe can complete 2/3 of the job in one hour, then it will take him 3/2 hours to complete the job.
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Let's use these rules to solve the question. . . .

Carl can wash all the windows of his house in 6 hours.
So, Rule #1 tells us that Carl can wash 1/6 of the windows in ONE HOUR

Maggie can wash all the windows in 4 hours
Rule #1 tells us that Maggie can wash 1/4 of the windows in ONE HOUR

Their COMBINED rate = 1/6 + 1/4 = 2/12 + 3/12 = 5/12
So, working TOGETHER, Carl and Maggie can wash 5/12 of the windows in ONE HOUR

How many hours will it take for both of them working together to wash all the windows?
If Carl and Maggie can wash 5/12 of the windows in ONE HOUR, then according to Rule #2, they can wash all of the windows in 12/5 hours

12/5 hours = 2 2/5 hours

Answer: C

Cheers,
Brent

M7MBA wrote:Carl can wash all the windows of his house in 6 hours. His wife Maggie can wash all the windows in 4 hours. How many hours will it take for both of them working together to wash all the windows?

A. 2
B. 2 1/4
C. 2 2/5
D. 4 1/2
E. 5

[spoiler]OA=C[/spoiler]

Source: Princeton Review

Let T be the number of hours they work together to wash all the windows. We can create the equation:

T/6 + T/4 = 1

Multiplying by 12, we have:

2T + 3T = 12

5T = 12

T = 12/5 = 2 2/5

Answer: C

Hi All,

We're told that Carl can wash all the windows of his house in 6 hours and Maggie can wash all the windows in 4 hours. We're asked for the number of hours it would take for both of them working together to wash all the windows. This is a standard version of a Work Formula question, so we just need to plug in those two numbers and do a simple calculation to answer this question.

Work = (A)(B)/(A+B) where A and B are the times it takes the two individuals to complete the task on their own

(6)(4)/(6+4) = 24/10 hours to complete the task together. 24/10 hours = 2 4/10 = 2 2/5 hours

Final Answer: C

GMAT assassins aren't born, they're made,
Rich