Speed, Distance and Time

Averages

N1/L2.4

HD1/E3.1

Speed, Distance And Time

Speed (1)

m.p.h. means miles per hour

k.p.h. means kilometres per hour

· In 2 hours a snail crawls 20cm

so in 1 hour it crawls 10cm.

Therefore its speed is 10cm per hour.

· In 2 hours a car travels 100 miles

so in 1 hour it travels 100 miles ¸ 2 = 50 miles

This (50 m.p.h.) is its speed.

You can see that to find SPEED we divide the DISTANCE travelled by the TIME it takes.

SPEED = DISTANCE ¸ TIME

· A plane travels 1200 km in 3 hours

Its speed is 1200 ¸ 3

= ______k.p.h.

· Brian walks 15 miles in 5 hours

What is his speed in miles per hour?

15 ¸ 5

= ______m.p.h.

Now find the speed that these travel at:

1) Carmel leaves her house at 8.00 am

By 10.00 am she has travelled 74 miles

What is her speed?

2) A truck travels 195 kilometres in 3 hours.

What is its speed?

3) Julie travels from Leicester to Perth (324 miles) in 6 hours.

What is her speed?

4) A train takes 5 hours to travel 265 miles.

What is its speed?

5) Brian walks for a day in the dales. In 7 hours he covers

24.5 miles.

What is his speed?

6) Kevin drives a long distance coach. Here is his log

Find the average speed for each journey.

Departure Time / Arrival
Time / Mileage / Speed
a) / Swansea / Aberystwyth / 76 miles / ____ m.p.h.
9.00 am / 11.00 am
b) / Aberystwyth / Shrewsbury / 73 miles / ____ m.p.h.
11.30 am / 1.30 pm
c) / Shrewsbury / Cardiff / 108 miles / ____ m.p.h.
2.30 pm / 5.30 pm
d) / Cardiff / Swansea / 41 miles / ____ m.p.h.
5.30 pm / 6.30 pm

Check your answers, then discuss with your tutor what you need to work on next.

Answers

Speed, Distance And Time

Speed (1)

· 400 k.p.h.

· 3 m.p.h.

1) 37 m.p.h.

2) 65 m.p.h.

3) 54 m.p.h.

4) 53 m.p.h.

5) 3.5 m.p.h. (or 3½ m.p.h.)

6) a) 38 m.p.h.

b) 36.5 m.p.h.

c) 36 m.p.h.

d) 41 m.p.h.

Speed, Distance And Time

Speed (2)

Have a look at this example:

What is my speed if I drive 25 miles in 30 minutes?

(Remember speed is miles per hour)

30 minutes ® 25 miles

So in 1 hour I travel 50 miles

My speed is 50 miles per hour

Try this one …

· A train travels from Liverpool to Manchester in 45 minutes.

The distance is 36 miles. What is the speed of the train?

36 miles in 45 minutes

____ miles in 15 minutes (divide by 3)

____ miles in 60 minutes (multiply by 4)

so ____ miles per hour

What about this one?

· I can run a mile in 10 minutes

What is my speed?

1 mile in 10 minutes

___ miles in 60 minutes

so ____ miles per hour

Now follow this example:

Sandra walks 6 miles in 1½ hours

What is her speed?

We want to know how far she walks in 1 hour (this will be her

speed in m.p.h.).

So 6 miles in 1½ hours

2 miles in ½ hour

Now we know how far she walks in ½ hour we can double it to find her speed:

So 2 miles in ½ hour

4 miles in 1 hour

Her speed is 4 m.p.h.

Complete these:

· Joe drives 150 miles in 2½ hours

What is his speed?

150 miles in 2½ hour

___ miles in ½ hour

So ______miles in 1 hour

= ______m.p.h.

· A jet travels 400 km in 1¼ hours

What is its speed?

400 miles in 1¼ hours

____ miles in ¼ hour

____ miles in 1 hour

= ____ m.p.h.

A) 1) Terry walks to work. He goes 2 miles in 30 minutes.

What is his speed in m.p.h.?

2) The distance from Leeds to Bradford is 10 miles. In rush hour it takes 30 minutes for Pete to make the journey

What speed is Peter travelling at?

3) A train takes 2½ hours to travel between London and Swansea (190 miles)

What is the train's speed?

4) Find the speed of a car that travels:

a) 15 miles in 20 minutes

b) 69 miles in 1½ hours

c) 14 miles in ¼ hour

d) 39 miles in ¾ hour

5) Look at the map of distances from Manchester, then answer the following questions:

A delivery van makes these journeys during the week. Find out what its speed is.

From / To / Time taken / Speed
Mon / Manchester / Leeds / 50 mins
Tues / Manchester / Carlisle / 2 hours
Wed / Manchester / Birmingham / 1 hr 30 mins
Thurs / Manchester / Middlesborough / 2 hrs 15 mins
Fri / Manchester / London / 3 hrs 20 mins
Sat / Manchester / Liverpool / 45 mins

v v v v v

You may need to work out the Average speed travelled.

To do this first add up the total distance travelled and the total time spent travelling.

Then work out as usual:

AVERAGE SPEED = TOTAL DISTANCE ¸ TOTAL TIME

For example

I walk 9 miles in 2 hours, then I catch a bus for 75 miles which takes 2 hours. What is my average speed?

9 miles + 75 miles = 84 miles

2 hrs + 2 hrs = 4 hrs

84 ¸ 4 = 21 m.p.h.

B) Try these:

1) A train travels 60 miles in 1 hour, stops for 45 minutes, and then goes 75 miles for 1¼ hours

What is the average speed?

2) Look at the bus timetable

What is the average speed of the bus?

10 MILES 11 MILES 15 MILES 24 MILES

Arrive / Depart
Bedale / Fellhead / Minton / Minton / Inthwaite / Skipwith
10.20 / 10.42 / 11.05 / 11.35 / 12.10 / 13.00

3) Jean cycles 25 km in 4 hours. She gets a puncture and walks to the bus stop. The bus takes an hour to cover 45 km.

What is her average speed?

4) Denis races his car on a long distance race

Find out his speed for each stage then work out his average speed (round off).

1st stage 216 miles in 3 hrs

2nd stage 180 miles in 2 hrs 30 mins

3rd stage 88 miles in 1 hour 6 mins

4th stage 40 mile in 30 mins

5th stage 77 miles in 1 hour 24 mins

C) Average Speed on the Motorway

1) A motorist drives from Liverpool to Sheffield direct on the motorway and takes approximately one and a half hours.

Use the mileage chart below to find the distance she travels, and try working out her average speed.

2) on the return journey she intends to drive via Nottingham back to Liverpool. She reckons she will average about 30 m.p.h., as only part of her journey is on the motorway.

Use the chart to find out how many miles she will travel.

How long should the driving take?

3) The journey goes as planned. What was the total distance travelled over the whole journey from Liverpool to Sheffield and back?

How long did the whole journey take altogether?

What was the motorist's average speed over the whole journey?

MILEAGE CHART

Liverpool

36 Manchester

155 132 Newcastle

220 185 264 Norwich

98 63 157 122 Nottingham

157 144 250 145 98 Oxford

283 283 410 343 276 185 Plymouth

234 221 337 186 175 72 164 Portsmouth

72 38 125 146 37 135 283 212 Sheffield

Check your answers, then discuss with your tutor what you need to work on next.

Answers

Speed, Distance And Time

Speed (2)

· 48 m.p.h.

· 6 m.p.h.

· 60 m.p.h.

· 320 k.p.h.

A) 1) 4 m.p.h.

2) 20 m.p.h.

3) 76 m.p.h.

4) a) 45 m.p.h. 5) Mon 54 m.p.h.

b) 46 m.p.h. Tues 58.5 m.p.h.

c) 56 m.p.h. Wed 60 m.p.h.

d) 52 m.p.h. Thurs 48 m.p.h.

Fri 60 m.p.h.

Sat 48 m.p.h.

B) 1) 45 m.p.h.

2) 22.5 m.p.h.

3) 14 m.p.h.

4) 1st 72 m.p.h.

2nd 72 m.p.h.

3rd 80 m.p.h.

4th 80 m.p.h.

5th 55 m.p.h.

Average speed 70.7 m.p.h.

C) 1) 72 miles 48 m.p.h.

2) 135 miles 4 hrs 30 mins

3) 207 miles 34.5 m.p.h.