Linear Equation Word Problems

Question

Alma and Erika work part-time stocking shelves at a grocery store. At 7:00 a.m on Saturday, Alma begins unpacking boxes at a rate of 1 box every 6 minutes. Erika joins her at 7:45 a.m unpacks 1 box every 5 minutes. When finished with this task, a total of 24 boxes have been unpacked since 7:00 a.m. If x represents the number of minutes for which Alma has been working, which of the following equations best models the situation?

Answer Choices:

A. 1/6x+1/5​(x−45)=24

B. 1/6x+1/5(x-3/4)=24

C. 6x+5(x−45)=24

D. 6x+5(x−3/4)=24

Answer 1

Since the units of time is in minutes and not hours, we can ignore the choices with 3/4 and consider the choices with 45 minutes.

The total of 24 is the number of boxes is the combination of the two workers unpacking boxes. So we need to know how many 6 minutes periods are in the total time Alma worked, x, and how many 5 minutes periods are in the total time Erika worked, x-45. This requires division. So the answer is A.