A runner runs 400 m to the nearest m in 80 s to the nearest s. Find…

Step by step

The question

Question: A runner goes 400 m (to the nearest m) in 80 s (to the nearest s).

Find the upper bound of the speed.

1 Bounds of each number

The distance is 400 m, to the nearest m.

Half a step is 0.5.

So it is from 399.5 up to 400.5.

The time is 80 s, to the nearest s.

Half a step is 0.5.

So it is from 79.5 up to 80.5.

2 Choose the bounds

Dividing by a bigger number gives a smaller answer.

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

So we use 400.5 and 79.5.

Careful!

A bigger bottom makes the answer smaller.

So the bottom goes the other way.

3 Work it out

With a calculator: about 5.04 m/s, to 3 significant figures.

So the upper bound of the speed is 5.04 m/s.

4 Check

Let's check.

With the rounded numbers we get 5.

The upper bound, 5.04, is more 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.