Jason can stack two shelves in 3 hours and Maria can stack

Hi All,

We're told that Jason can stack 2 shelves in 3 hours and Maria can stack 3 shelves in 2 hours. We're asked how long will it take them together, working at their constant rates, to stack thirteen shelves. This question is a 'rate' question, so you can work through the math in a number of different ways. Here's an approach that puts both rates in terms of 'output per hour':

Jason stacks 2 shelves every 3 hours, so he stacks 2/3 of a shelf per hour.
Maria stacks 3 shelves every 2 hours, so he stacks 3/2 of a shelf per hour.
Combined, they stack 2/3 + 3/2 = 4/6 + 9/6 = 13/6 shelves per hour.

We're asked how long it would take for the two to stock 13 shelves....

(X)(13/6 shelves/hour) = 13 shelves
X = 13(6/13) = 6 hours

Final Answer: B

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

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Let each shelf = 6 pounds.
Since Jason takes 3 hours to stack 2 6-pound shelves -- for a total of 12 pounds -- Jason's rate = 12/3 = 4 pounds per hour.
Since Maria takes 2 hours to stack 3 6-pound shelves -- for a total of 18 pounds -- Maria's rate = 18/2 = 9 pounds per hour.
Total weight of 13 6-pound shelves = 13*6 = 78 pounds.
Combined rate for Jason and Maria = 4+9 = 13 pounds per hour.
Time for Jason and Maria to stack the 13 shelves = 78/13 = 6 hours.

The correct answer is B.

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The combined rate of Jason and Maria is 2/3 + 3/2 = 4/6 + 9/6 = 13/6.

So it takes them 13/(13/6) = 13 x 6/13 = 6 hours to stack 13 shelves.

Answer: B

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Jeffrey Miller Head of GMAT Instruction