Ratio, proportion and percentages
Ratio, proportion and percentages

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Ratio, proportion and percentages

1.5.1 Try some yourself

Activity 8

Which is greater, 1.2 minutes or 70 seconds?

Answer

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.

Activity 9

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.)

Answer

  • (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.)

Activity 10

Which is longer, 11 minutes or 0.17 hours?

Answer

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.)

Activity 11

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.

Answer

  • (a)

    • (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).

  • (b)

    • (i) 70 × = 175 km.

    • (ii) 2.29 hours (2 hours 17 minutes).

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