Routes: distance, speed and time · Grade 10 · 3 units
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
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
Not on the site yet
Parts of this topic that are not built 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, so there are new exercises every time. The topic follows the Israeli Ministry of Education’s high school maths curriculum at 3 units (grades 10 and 11).