A runner runs 100 m to the nearest m in 12 s to the nearest s. Find…

Step by step

The question

Question: A runner goes 100 m (to the nearest m) in 12 s (to the nearest s).

Find the lower bound of the speed.

1 Bounds of each number

The distance is 100 m, to the nearest m.

Half a step is 0.5.

So it is from 99.5 up to 100.5.

The time is 12 s, to the nearest s.

Half a step is 0.5.

So it is from 11.5 up to 12.5.

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 99.5 and 12.5.

Careful!

A smaller bottom makes the answer bigger.

So the bottom goes the other way.

3 Work it out

That is 7.96 m/s.

So the lower bound of the speed is 7.96 m/s.

4 Check

Let's check.

With the rounded numbers we get 8.33.

The lower bound, 7.96, 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.