Problem Solving

swerve wrote:Working independently San can complete a certain job in 5 hours and Diane can complete the same job in x hours. If working together Sam and Diane can complete the job in 3 hours, what is the value of x?

A. 20
B. 12
C. 8
D. 7.5
E. 4

Sam's rate is 1 job in 5 hours, or 1/5. Diane's rate is 1 job in x hours, or 1/x. The sum of Sam's individual rate and Diane's individual rate is their combined rate, which is 1 job in 3 hours, or 1/3. Thus, we can create the equation:

1/5 + 1/x = 1/3

Multiplying by 15x we have:

3x + 15 + 5x

2x = 15

x = 7.5

Answer: D

Hi swerve,

We're told that, working independently Sam can complete a certain job in 5 hours, Diane can complete the same job in X hours and working together the two can complete the job in 3 hours. We're asked for the value of X. This is an example of a standard "2 entity" question that can be solved with the Work Formula:

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

Since we have the rates of the two people - and the end result - we can plug all of that information into the Work Formula:

(5)(X)/(5+X) = 3
5X = 15 + 3X
2X = 15
X = 7.5 hours

Final Answer: D

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