# Routes: distance, speed and time · Year 10

> Routes: distance, speed and time, Year 10: The length of a route and more. Explanation, worked examples and free practice for the national curriculum in England.

In Routes: distance, speed and time (Year 10) you practise 4 skills: The length of a route · Distance, speed and time · Comparing routes · Planning a route.

A route is made of straight parts and arcs of circles. The length of a route is the sum of the lengths of all its parts. The perimeter of a shape is a route that goes round it, and a semicircle is half the circle’s circumference.

Distance equals speed times time. When you know two of the three, you can find the third: the time is the distance divided by the speed, and the speed is the distance divided by the time. A speed in km/h is the number of kilometres travelled in one hour.

Before you work it out, check the units match: a kilometre is 1,000 metres, and an hour is 60 minutes. The average speed of a trip is the whole distance divided by the whole time.

When you choose between routes, compare what matters at the time: the length, the time or the cost, such as fuel and tolls.

**Tip:** Sketch the route and write each part’s length on it, then write the unit beside every number.

## What you learn

### The length of a route

- Example: A walking route goes all the way round a rectangular park. (A rectangular park with the lengths of two neighbouring sides) The lengths are in metres. How long is one lap of the park?
- Answer: 364 m
- Solution: One lap is the perimeter of the park: 2 × (144 + 38) = 364

### Distance, speed and time

- Example: A car travelled 200 km in 4 hours, at a steady speed. What was its speed?
- Answer: 50 km/h
- Solution: Speed is distance divided by time: 200 ÷ 4 = 50 (A table: the speed, time and distance of each car.)

### Comparing routes

- Example: There are two ways to drive from home to the beach. (A table of the length and the speed of the two routes) Which route is quicker?
- Options: Route A · Route B
- Answer: Route B
- Solution: Route A: 111 ÷ 60 × 60 = 111 minutes. Route B: 150 ÷ 100 × 60 = 90 minutes.

### Planning a route

- Example: One lap of a running track is 500 metres. How many laps make 11.5 km?
- Answer: 23
- Solution: The distance in metres: 11.5 × 1000 = 11500 . The laps: 11500 ÷ 500 = 23

The exercises are made by rules and the answers are worked out in code. The topic follows the national curriculum in England: mathematics (key stages 3 and 4).

[Practise on the site](https://kixplo.com/uk/en/) · [All Year 10 topics](https://kixplo.com/uk/en/maths/year-10/)