# Problem of the Week

Problem C and Solution

Lawn Care

## Problem

Lawns â€˜Râ€™ Us is a company that specializes in lawn care. When mowing lawns, they use both a powerful riding lawn mower and a push lawn mower. For a certain lawn, it takes the company \(3\) hours to cut the entire lawn using the push lawn mower only, and \(40\) minutes to cut the entire lawn using the powerful riding lawn mower only.

One day, the powerful riding lawn mower broke down after \(90\%\) of the lawn was cut. The remainder was then cut using the push lawn mower.

How many minutes did it take the company to cut the entire lawn?

## Solution

It takes the company \(40\) minutes to cut \(100\%\) of the lawn with the powerful riding lawn mower. Therefore, it would take \(90\%\) of \(40\) minutes or \(0.90\times 40=36\) minutes to cut \(90\%\) of the lawn with the powerful riding lawn mower.

Since \(90\%\) of the lawn is cut with the powerful riding lawn mower, then \(100\%-90\%=10\%\) of the lawn remains to be cut with the push lawn mower. It takes \(3\) hours or \(3\times 60=180\) minutes to cut \(100\%\) of the lawn with the push lawn mower. Therefore, it would take \(0.10\times 180=18\) minutes to cut \(10\%\) of the lawn with the push lawn mower.

Therefore, it would take a total of \(36+18=54\) minutes to cut the entire lawn using the powerful riding lawn mower for \(90\%\) of the job and the push lawn mower for \(10\%\) of the job.