# Problem of the Week Problem A and Solution Bicycle Time

## Problem

Mr. Turnblatt’s bicycle needs to be serviced every $$600$$ km. Each year, he rides his bike between March and November for $$35$$ consecutive weeks, $$5$$ days a week, $$8$$ km a day.

1. If he has his bike serviced before his first trip of the year, how many weeks will it be until his bicycle needs the next service?

2. How many times will he have his bike serviced in one year?

## Solution

1. Since Mr. Turnblatt rides his bike $$5$$ days a week and $$8$$ km a day, then in one week he travels $$5 \times 8 = 40$$ km.

We can skip count by $$40$$ to see how many weeks it takes to get to $$600$$ km: $40, 80, 120, 160, 200, 240, 280, 320, 360, 400, 440, 480, 520, 560, 600$ So after $$15$$ weeks Mr. Turnblatt will have ridden $$600$$ km and will need to have his bike serviced.

Alternatively, we could have divided $$600 \div 40 = 15$$ to determine that it takes Mr. Turnblatt $$15$$ weeks to ride $$600$$ km.

2. From part (a), we know that his bicycle needs to be serviced every $$15$$ weeks. So, the bike needs to be serviced at the end of Week $$15$$ and at the end of Week $$30$$. After that, since there are only $$5$$ more weeks of biking, the bike does not need to be serviced until the following year.

Counting the service before the first trip of the year, Mr. Turnblatt will need to have his bike serviced $$3$$ times in a year.