# 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.