Question

In the summer term, Sal walks to school starting soon after 7 am when the hour hand is at an angle of 110° to the minute hand.She arrives at school before 8 am when the hands are again at an angle of 110° to each other.How many minutes does she take to walk to school?

Answer 1

41 minutes

Explanation:

Consider the diagram below:

The angle between the hour and minute hand = 30°+80°=110°

We determine the time she starts below:

`\begin{gathered} \text{A rotation by }90\degree\text{ moves the minute hand 15 minutes} \\ \implies\text{A rotation by 1}\degree\text{ moves the minute hand }\frac{\text{15}}{90}\text{ minutes} \\ \implies\text{A rotation by 100}\degree\text{ moves the minute hand }\frac{\text{15}}{90}*100 \\ \approx17\text{ minutes} \end{gathered}`

She left home at 7:17 AM.

Next, we determine the time she arrived at school.

`\implies\text{A rotation by 10}\degree\text{ moves the minute hand }\frac{\text{15}}{90}*10\approx2\text{ minutes}`

This means that she arrived at school at 7:58 AM.

Therefore, the number of minutes she takes to walk to school will be:

`\begin{gathered} 7\colon58-7\colon17 \\ =41\text{ minutes} \end{gathered}`

It