1.5.1 Try some yourself
Which is greater, 1.2 minutes or 70 seconds?
There are at least three ways of answering this:
(a) 70 seconds is = 1.1666 ... minutes, which is less than 1.2 minutes.
(b) 1.2 minutes is = minutes. 70 seconds is 1 minute 10 seconds, i.e. = minutes. Since is less than , 70 seconds is less than 1.2 minutes.
(c) 1.2 minutes is 1.2 × 60 = 72 seconds, which is greater than 70 seconds.
So 1.2 minutes is greater than 70 seconds.
Answer the following questions:
(a) A cheetah is the fastest land animal over short distances. It can run 400 metres in 15 seconds. What would be its speed in metres per second and kilometres per hour?
(b) The slowest moving land animal is the three-toed sloth from tropical America. It takes 16 hours to travel a mile. What is this speed in kilometres per hour and in metres per second? (5 miles is approximately 8 km.)
(a) Speed is the ratio of distance travelled to time taken, which in the cheetah's case is 400 metres to 15 seconds. So its speed is 27 metres per second (to 2 s.f.).
To determine this speed in kilometres per hour, both units need changing.
400 metres are kilometres
15 seconds are hours.
So in the new units is
So the cheetah's speed is 96 kilometres per hour (over a distance of 400 metres).
(b) In 16 hours the sloth moves 1 mile.
It will take 5 × 16 = 80 hours to move 5 miles which is 8 km.
So it will take 80 hours to move 8 km.
In 1 hour it will move 8/80 km or 0.1 km.
So the sloth will move at a speed of 0.1 km/h (assuming it does not fall asleep!).
To convert this speed to metres per second,
0.1 km is 100 metres
1 hour is 3600 seconds
So speed is 0.028 metres per second (to 2 s.f.)
Which is longer, 11 minutes or 0.17 hours?
As a fraction of an hour, 11 minutes is 11/60 hours.
To convert this to a decimal, divide 11 by 60 to get 0.18333….
This is greater than 0.17, so 11 minutes is longer.
(Alternatively, 0.17 hours is 60 × 0.17 = 10.2 minutes, so 11 minutes is longer.)
A van driver averages 50 km per hour travelling on ordinary roads and 70 km per hour on motorways. Estimate:
(i) how far the van will travel in hours;
(ii) how long it will take to travel 160 km;
when travelling on (a) ordinary roads and (b) motorways.
(i) In 1 hour the van travels 50 km so in hours the van travels 50 × = 125 km.
(ii) The van travels 50 km in 1 hour so it travels 1 km in hour. It therefore travels 160 km in 160 × hours, i.e. hours or hours (3 hours 12 minutes).
(i) 70 × = 175 km.
(ii) 2.29 hours (2 hours 17 minutes).