Page 132 - ICSE Math 7

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Example 8: A deer pursues a fawn at a speed of 30 km h , while the fawn runs at a speed of
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12 km h . After what distance and how much time will the deer be able to catch the
fawn if the fawn is 75 m ahead of the deer?
Solution: As deer and fawn are running in the same direction, their relative speed = (30 – 12) km h –1

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= 18 km h = 18 × 5 = 5 m s .
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Time required to catch the fawn = 75 s = 15 s
5
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Speed of the deer in m s = 30 × 5 = 25 m s –1
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Distance covered by the deer in 15 s = 25 × 15 m = 125 m
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Example 9: A train 160 m long crosses a person in 4 s. Determine
its speed in: Maths Info
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(a) m s (b) km h –1 To pass a pole or a person, a
Solution: Distance travelled by the train = Length of the train train has to travel a distance
equal to its own length.
= 160 m
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(a) Speed of the train in m s = Distance = 130 m s = 32.5 m s –1
Time 4
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(b) Speed of the train in km h = 32.5 × km h = 117 km h –1
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Example 10: A train 180 m long, crosses a 240 m long bridge in 12 seconds. Find:
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(a) the speed of the train in km h .
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(b) the time taken by the train to pass a man running in the direction of the train at 6 km h .
Solution: (a) Distance travelled by the train = Length of the train + length of the bridge
= 180 m + 240 m Maths Info
= 420 m
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Speed of the train in m s = Distance = 420 m s –1 To pass a platform or a bridge, a
train has to travel a distance equal
Time 12
= 35 m s –1 to the sum of its own length and
that of platform or bridge.
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Speed of the train in km h = 35 × 5 km h = 126 km h –1
(b) Since both the train and the man are running in the same direction, therefore their
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relative speed is (126 – 6) km h = 120 km h = 120 × 5 = 100 m s .
Distance travelled = Length of the train = 180 m 18 3
180 180 × 3 540 2
Time taken = s = s = s = 5 s
100/3 100 100 5
Example 11: Two trains A and B, 120 m and 180 m long are moving along parallel tracks with speeds
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80 km h and 90 km h respectively. How long will train A take to overtake train B?
Solution: Distance to be covered by train A
= Sum of the lengths of the trains A and B Maths Info
= 120 m + 180 m = 300 m To pass or overtake another
Time required by train A to overtake train B train, a train has to travel a

300 × 18 80 × 5 distance equal to the sum of
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= s = 13.5 s (80 km h = m s ) the lengths of the two trains.
80 × 5 18
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