Speed, distance and time
Use the formula to find speed, distance or time, convert between units, and solve multi-step journey problems.
Worked examples
Finding time using $s = d \div t$
Straightforward
Problem
A train travels 350 km at a constant speed of 70 km/h. How long does the journey take?
1
Write the formula for time.
2
Substitute the known values.
3
Calculate.
Answer
The journey takes 5 hours.
Converting km/h to m/s
Moderate
Problem
A car travels at 108 km/h. Convert this speed to m/s.
1
Identify the conversion factors.
1 km = 1000 m and 1 hour = 3600 s, so to convert km/h to m/s, multiply by .
2
Multiply by the conversion factor.
3
Verify by converting back.
Answer
108 km/h = 30 m/s
Average speed for a return journey
Challenging
Problem
A car travels 240 km from city A to city B at 80 km/h, then returns along the same route at 60 km/h. Find the average speed for the entire journey.
1
Find the time for each leg of the journey.
2
Find the total distance and total time.
3
Apply the average speed formula.
4
Note: the average speed is not simply the average of 80 and 60.
The average of 80 and 60 would give km/h, but the car spends more time at the slower speed, so the true average is less than 70 km/h.
Answer
The average speed is km/h.
Practise
Q1·Straightforward
A car travels 240 km in 3 hours. What is its speed in km/h?
Explanation
Q2·Straightforward
A cyclist rides at 20 km/h for 2.5 hours. How far does the cyclist travel in km?
Explanation
Q3·Straightforward
A runner travels 15 km at a constant speed of 5 km/h. How many hours does the run take?
Explanation
Q4·Straightforward
A train travels 450 km at 90 km/h. How many hours does the journey take?
Explanation
Q5·Moderate
Convert 72 km/h to m/s.
Explanation
1 km = 1000 m and 1 hour = 3600 s, so:
Q6·Moderate
Convert 25 m/s to km/h.
Explanation
Q7·Moderate
A car travels 120 km at 60 km/h, then a further 80 km at 40 km/h. Find the total time taken in hours.
Explanation
Time for first leg: hours
Time for second leg: hours
Time for second leg: hours
Q8·Moderate
A cyclist rides at 15 km/h for 2 hours, then at 20 km/h for a further 1.5 hours. Find the total distance in km.
Explanation
Distance for first leg: km
Distance for second leg: km
Distance for second leg: km
Q9·Challenging
A car travels 180 km from town A to town B at 60 km/h, then returns along the same route at 90 km/h. Find the average speed for the entire journey in km/h.
Explanation
Time from A to B: hours
Time from B to A: hours
Total distance: km
Total time: hours
Time from B to A: hours
Total distance: km
Total time: hours
Q10·Challenging
A car and a bus both travel from city P to city Q, a distance of 180 km. The car travels at 90 km/h and the bus at 60 km/h. How many hours sooner does the car arrive than the bus?
Explanation
Car's travel time: hours
Bus's travel time: hours
Bus's travel time: hours
Q11·Challenging
A cyclist rides 60 km to town at 20 km/h, then returns along the same route at 30 km/h. Find the average speed for the round trip in km/h.
Explanation
Time riding to town: hours
Time returning: hours
Total distance: km
Total time: hours
Time returning: hours
Total distance: km
Total time: hours
Q12·Challenging
Two cyclists leave the same place at the same time and travel in the same direction. One rides at 18 km/h and the other at 12 km/h. How many hours does it take for them to be 30 km apart?
Explanation
The gap between the cyclists grows at:
Time for the gap to reach 30 km:
Time for the gap to reach 30 km: