A cyclist travels 60 km to the nearest 10 km in 2.5 h to the nearest…

Step by step

The question

Question: A cyclist goes 60 km (to the nearest 10 km) in 2.5 h (to the nearest 0.1 h).

Find the lower bound of the speed.

1 Bounds of each number

The distance is 60 km, to the nearest 10 km.

Half a step is 5.

So it is from 55 up to 65.

The time is 2.5 h, to the nearest 0.1 h.

Half a step is 0.05.

So it is from 2.45 up to 2.55.

2 Choose the bounds

Dividing by a bigger number gives a smaller answer.

So the smallest speed is the smallest distance divided by the biggest time.

So we use 55 and 2.55.

Careful!

A smaller bottom makes the answer bigger.

So the bottom goes the other way.

3 Work it out

With a calculator: about 21.6 km/h, to 3 significant figures.

So the lower bound of the speed is 21.6 km/h.

4 Check

Let's check.

With the rounded numbers we get 24.

The lower bound, 21.6, is less than that, as it should be.

So the answer is right!

Let's look back.

First: bounds of each number.

Then: choose the bounds.

Then: work it out.

Last: check.