Routes: distance, speed and time · Year 10
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
For example: A walking route goes all the way round a rectangular park. The lengths are in metres. How long is one lap of the park?
Answer and solution
The answer: 364 m
One lap is the perimeter of the park: 2 × (144 + 38) = 364
Distance, speed and time
For example: A car travelled 200 km in 4 hours, at a steady speed. What was its speed?
Answer and solution
The answer: 50 km/h
Speed is distance divided by time: 200 ÷ 4 = 50
| Speed (km/h) | Time (hours) | Distance (km) | |
|---|---|---|---|
| The car | 50 | 4 | 200 |
Comparing routes
For example: There are two ways to drive from home to the beach.
| Route | Length (km) | Speed (km/h) |
|---|---|---|
| A | 111 | 60 |
| B | 150 | 100 |
- Route A
- Route B
Answer and solution
The answer: Route B
Route A: 111 ÷ 60 × 60 = 111 minutes. Route B: 150 ÷ 100 × 60 = 90 minutes.
Planning a route
For example: One lap of a running track is 500 metres. How many laps make 11.5 km?
Answer and solution
The answer: 23
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, so there are new exercises every time. The topic follows the national curriculum in England: mathematics (key stages 3 and 4).