### Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

### Calendar Capers

Choose any three by three square of dates on a calendar page...

### Days and Dates

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

# Hiking the Hill

##### Stage: 3 Short Challenge Level:

Suppose the path is $x$ miles long. Then she takes $\frac{1}{2}x$ hours to walk up the hill, and another $\frac{1}{4}x$ hours to walk back down. Therefore, in $\frac{3}{4}x$ hours she walks a total distance of $2x$.

This means her average speed is $(2x) \div (\frac{3}{4}x) = \frac{8}{3} = 2\frac{2}{3}$ miles per hour.

This problem is taken from the UKMT Mathematical Challenges.