# 3.5 Combining formulas

There is a quicker way to the answer which requires two of the formula to be combined to give a new formula for relative stride length.

The formula for relative stride length was:

It is known that:

This means that it is possible to substitute the formula for hip height in the formula for relative stride length. This then gives:

This new formula could be used directly with the information that was given in the question. This version would also make more sense in the field, as it contains the two pieces of information that would be known on site.

In the final activity for this week you’ll consider why it is important to always think about whether the answer you have obtained looks sensible. This is something that you should always ask yourself. It can act as a prompt to check over your working or logic in any problem.

## Activity 11 Relative stride length: what’s wrong?

A student used the formula to calculate the relative stride length in the footprints activity.

The student entered the key sequence on their calculator for the calculation as: 104.6 ÷ 4 × 21.8. This gave an answer of approximately 570, so the student concluded that the person was probably running very fast. Can you explain where the student made the mistake and why they should have been suspicious of their answer?

### Answer

The calculator will perform this calculation from left to right, using the BEDMAS rules (order of operations), which treat multiplication and division as equally important. So, it will first divide 104.6 by 4 to get 26.15, and then multiply by 21.8 to get approximately 570. However, this is not the correct calculation from the formula.

The stride length (104.6) should be divided by (4 × foot length), so the calculation should be 104.6 ÷ (4 × 21.8). When explaining the formula at the start of this section you were told that the expected value for relative stride length lies between 0 and 5. So, an answer of 570 should have immediately set alarm bells ringing for this student that something had gone wrong somewhere. As well as checking your answer using known information, carrying out a quick estimate of what size of answer you are expecting can also be very useful. So, if you are expecting a value in the order of hundreds, say around 200, and your answer is in the millions, then those alarm bells should be ringing again!

Well done, you’ve just completed the last activity for Week 3! You’ve just got one final section to look at before moving on to the Week 3 quiz. This summarises the top tips for using any formula that you've covered here.