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This video is for the redesigned SAT which is for you if you are taking the SAT in March 2016 and beyond.

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Passport to Advanced Math

\(\frac{1}{x} + \frac{2}{x} = \frac{1}{5}\)

Anise needs to complete a printing job using both of the printers in her office. One of the printers is twice as fast as the other, and together the printers can complete the job in 5 hours. The equation above represents the situation described. Which of the following describes what the \(\frac{1}{x}\) expression represents in this equation?

A) The time, in hours, that it takes the slower printer to complete the printing job alone

B) The portion of the job that the slower printer would complete in one hour

C) The portion of the job that the faster printer would complete in two hours

D) The time, in hours, that it takes the slower printer to complete \(\frac{1}{5}\) of the printing job

The correct answer is B) The portion of the job that the slower printer would complete in one hour.

The quickest method would be to recognize that the given equation is similar to the formula used for work problems:

If we let x be the time taken by the slower printer then the time taken by the faster printer would be \(\frac{1}{2}x\) since it is twice as fast. Substitute that into the work formula and we get

\(\frac{1}{x} + \frac{2}{x} = \frac{1}{5}\)

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