06/03/2020 (2011: National Sprint Round, Problem 6)

Q: The amount of time it takes to shovel the snow in a parking lot is inversely proportional to the number of men shoveling. If it takes 3 hours for 5 men to complete the job, how many hours would it take 2 men to complete the job? Express your answer as a decimal to the nearest tenth.

A: 7.5

The total amount of time it takes to complete the job is Time Taken ⋅ People On The Job. 3 hours were taken to complete the job and 5 people were working on it, so 3 * 5 = 15 hours are required to complete the job.

Because there are 2 people working on the job, we do 15 hours ÷ 2 people = 7.5 hours taken.