# Routes: distance, speed and time · Grade 10 · 3 units

> Routes: distance, speed and time, Grade 10 · 3 units: Comparing routes and more. Explanation, worked examples and free practice following the Israeli curriculum.

In Routes: distance, speed and time (Grade 10 · 3 units) 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

## Not on the site yet

- Planning a route on a map
- A speed that changes along the route

The exercises are made by rules and the answers are worked out in code. The topic follows the Israeli Ministry of Education’s high school maths curriculum at 3 units (grades 10 and 11).

[Practise on the site](https://kixplo.com/il/en/) · [All Grade 10 · 3 units topics](https://kixplo.com/il/en/math/grade-10-3u/)