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Work crews Alpha and Zeta are repaving a section of freeway in Los Angeles. Work crew Alpha started its work one week (40 working hours) earlier than work crew Zeta, and started on the north end of the freeway, working its way south at a rate of 12 meters per hour since starting the job. Now, work crew Zeta has started at the south end, working its way north at a rate of 10 meters per hour. The section of freeway that needs to be repaved is 1.5 kilometers long, including the section that has already been paved.

Given that each crew will not necessarily work the same number of hours, which of the following answer choices represents an hourly workload for each crew that will finish the project? Please make only one selection in each column.
Crew AlphaCrew ZetaNumber of Hours
10
20
30
40
50
60



The correct answer is:

Crew AlphaCrew ZetaNumber of Hours
  10
  20
 30
  40
  50
 60


To solve this problem, you must create a model that generates the potential solutions. The total distance paved by Crew Alpha is 12*A, and the total distance paved by Crew Zeta is 10*Z, where A and Z are the hours worked by the respective crews. Thus, the answer will be a solution to:

12A + 10Z = Distance To Be Paved

Note that 480 meters of highway have already been paved (12 meters/hour * 40 hours), so there are only 1020 meters remaining. This gives you:

12A + 10Z = 1020

By plugging in values from one column, you will be able to compare the result with values from the second column, and you will find that A = 60, Z = 30 gives you the correct answer.

12(60) + 10Z = 1020
10Z = 300
Z = 30