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4.2 Solving problems involving average speed

4.2 Solving problems involving average speed

If you know the total distance travelled and the total time You can only calculate with the
taken for a journey, you can work out the average speed average speed, as the actual speed
for the journey. over a journey changes all the time.
Use the formula: average speed = totaldistance
totaltime
which is usually written as: speed = distance Remember that these formulae are only
time
Two other versions of this formula are: true when the speed is constant.
distance = speed × time time = distance
speed

!is triangle can help you remember the three formulae.
D represents the distance, S the speed and T the time. D
D
D

!e triangle shows that: D = S × T S = T = .
T S

!e units for speed depend upon the units you are using for S × T
distance and time. For example:
t when the distance is measured in kilometres and the time is in hours, the speed is measured in
kilometres per hour (km/h)
t when the distance is measured in metres and the time is in seconds, the speed is measured in
metres per second (m/s).

Worked example 4.2
1
a It takes Omar 3 hours to drive a distance of 273 km. Work out his average speed.
4
b Kathy is an 800 m runner. She runs at an average speed of 6 metres per second (m/s).
How long does it take her to run 800 m at this speed? Give your answer in minutes and seconds.

1
a 3 hours = 3.25 hours First write the number of hours as a decimal.
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Speed = distance = 273 = 84 km/h Write down the formula you need to use. Substitute the
.
time 325 values into the formula and work out the answer.
Check: 270 = 90 km/h ! Check, using estimation. 90 km/h is close to the answer
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of 84 km/h, so the answer is probably correct.
b Time = distance = 800 = 133.33... seconds Write down the formula you need to use. Substitute the
speed 6 values into the formula and work out the answer.
= 133 seconds (nearest second) Round the answer to a sensible degree of accuracy.
2 minutes = 120 seconds Convert the answer in seconds into minutes and seconds.
So 133 seconds = 2 minutes 13 seconds
Check: 2 minutes 13 seconds = 133 seconds Use an inverse calculation to check.
Distance = 133 × 6 = 798 km ! 798 km is close to the answer of 800 km, so the answer
is probably correct.

) Exercise 4.2 For each question in this exercise show all your workings and check your answers.

1 A cyclist travels a distance of 116 km in 4 hours. What is his average speed?
1
2 A motorist drives at an average speed of 80 km/h. How far does she travel in 3 hours?
2
36 4 Length, mass, capacity and time