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Question 14 of 18

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M:N:MC:13

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Passport to Advanced Math

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1 over x plus 2 over x equals 1 fifth

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 expression 1 over x represents in this equation?

Select an Answer

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

Correct Answer: 
No

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

Correct Answer: 
Yes

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

Correct Answer: 
No

The time, in hours, that it takes the slower printer to complete 1 fifth of the printing job

Correct Answer: 
No

View Correct Answer

Choice B is correct. From the description given, 1 fifth is the portion of the job that the two printers, working together, can complete in one hour, and each term in the sum on the left side is the part of this 1 fifth of the job that one of the printers contributes. Since one of the printers is twice as fast as the other, 2 over x describes the portion of the job that the faster printer is able to complete in one hour and 1 over x describes the portion of the job that the slower printer is able to complete in one hour.

Choice A is not the correct answer. The student may have not seen that in this context, the rates (that is, the work completed in a fixed time) of the printers can be added to get the combined rate, but the times it takes each printer to complete the job cannot be added to get the time for both printers working together, since the time for printers working together is less than, not greater than, the times for each printer alone. Hence the terms in the sum cannot refer to hours worked. In fact, the time it would take the slower printer to complete the whole job is x hours.

Choice C is not the correct answer. The student may have seen that 1 over x is the smaller term in the sum, wrongly concluded that the smaller term must apply to the faster printer, and then assumed the 2 in the numerator of the second term implies the equation describes work completed in 2 hours. In fact, the portion of the job that the faster printer could complete in 2 hours is open parentheses 2 close parentheses open parentheses 2 over x close parentheses equals 4 over x.

Choice D is not the correct answer. The student may have correctly seen that the value 1 fifth on the right side refers to the portion of the job completed, but not seen that in this context, the rates (that is, the work completed in a fixed time) of the printers can be added to get the combined rate, but the times it takes each printer to complete the job cannot be added to get the time for both printers working together. Hence the terms in the sum cannot refer to hours worked. In fact, the time it takes the slower printer to complete 1 fifth of the job is x over 5 hours.

Question Difficulty: 
hard
Objective: 

Students must interpret an equation that models a real-world situation and be able to interpret the whole expression (or specific parts) in terms of its context.