# Don't Be Late

Mary is driving to Birmingham Airport. Using her average speed for the entire journey, find how long her journey took.

## Problem

Mary drove to Birmingham Airport at 45 miles per hour for the first two hours, and then at 70 miles per hour for the remainder of the journey.

Her average speed for the entire journey was 60 miles per hour.

How long did Mary's journey to Birmingham Airport take?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

## Student Solutions

**Answer**: 5 hours

**Balancing the speeds**

The average speed is 60 miles per hour.

speed | relative to average | |

first hour | 45 | 60$-$15 |

second hour | 45 | 60$-$15 |

third hour | 70 | 60 + 10 |

etc. | 70 | 60 + 10 |

Each hour, she makes up 10 miles

She will need to do this for 3 hours

**Using algebra**

Let the time for which Mary drove at 70 mph be $t$ hours.

Then the total distance covered was $45 \times 2 + 70 \times t$ miles.

As her average speed over $2+t$ hours was $60$ mph, the total distance travelled was $60(2+t)$ miles.

Therefore $90 +70t = 120 + 60 t$, that is $10t = 30$, that is $t=3$.

So in total Mary's journey took $5$ hours.