Working at their individual rates, Marcus and Latrell can build a certain brick house...

[BTGmoderatorLU]

Source: Princeton Review

Working at their individual rates, Marcus and Latrell can build a certain brick house in 7.5 and 5 hours, respectively. When they work together, they are paid $35 per hour. If they share their pay in proportion to the amount of work each does, then what is Marcus' hourly pay for building the house?

A. $3
B. $6
C. $7
D. $14
E. $21

The OA is D

[Jay@ManhattanReview]

Source: Princeton Review

Working at their individual rates, Marcus and Latrell can build a certain brick house in 7.5 and 5 hours, respectively. When they work together, they are paid $35 per hour. If they share their pay in proportion to the amount of work each does, then what is Marcus' hourly pay for building the house?

A. $3
B. $6
C. $7
D. $14
E. $21

The OA is D

Given that Marcus and Latrell can build a certain brick house in 7.5 and 5 hours, respectively; working together they will take reciprocal of (1/7.5 + 1/5) = 3 hours.

Total payment for 3 hours = $35*3 = $105

Since Marcus takes 7.5, while Latrell takes 5 hours, Marcus is less efficient than Latrell. The $105 would be divided between Marcus and Latrell in the proportion of 1/7.5 : 1/5, or in the proportion of 5 : 7.5.

Share of Marcus in $105 = 105*(5/(5 + 7.5) = $42

Marcus' hourly pay for building the house = 42/3 = $14

The correct answer: D

Hope this helps!

-Jay
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