# Friday Puzzler: The solution 12th May

By Morwenna Evans Monday, May 12, 2014

## The Question

On Friday, we asked you this question:

Helen rode her bike from home to the river, which is 4km away.

It took her 9 minutes. She rode home using a shorter route of 3 km.

This only took her 6 minutes.

What was Helen’s average speed, in km/h, for the trip to the river and back?

## The Solution:

There are two ways you can do this;

The first is you find average speed on way there and average speed on way back and then the average them both. So, the average of the way there can be found by doing 60 (the number of minutes in an hour) divided by 9 (the amount of time it took her) times by 4 (how far she travelled).

When you do (60÷9) x 4 = 26 2/3 . The reason we do this some because we have that speed = distance ÷ time and we need to keep the ratio ie. 4/9=x/60 where x is the distance per hour.
If we do the similar sum for the way back we get (60÷6)x3=30. But then we need to find the average of these speeds in proportion to the time spent at each speed we do this by the following method Do 26 2/3 x 9 (the amount of time spent at that speed) plus 28 1/3 x 6 (amount of time at that speed) ÷15 (total time).

Once you have done this you get the answer of 28.

The far simpler way of doing this is by calculating the average of the total journey which is done by simply adding the time for each way and the length of each way and then finding that speed.

So the total of both the times is 15 minutes and the total distance is 7km. This speed amounts to 28km/h as 15 minutes is ¼ of an hour so to find how far Helen could ride in an hour you simply have to multiply 7 by 4; which is again 28.