Page 131 - ICSE Math 7

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5. A truck travels some distance at a speed of 35 km h in 120 min and the remaining distance at
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a speed of 48 km h in 90 min. Determine the:
(a) total distance covered. (b) average speed over the entire journey.
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6. A bus covers a total distance of 740 km, out of which it covers 156 km at 52 km h , 146 km at
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the speed of 36.5 km h and it covers the remaining distance in 5 hours. Determine:
(a) speed of bus to covers remaining distance.
(b) average speed of bus for the whole journey.
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7. An aeroplane goes from country A to country B with an average speed of 450 km h and returns
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with an average speed of 300 km h . Find the distance between the two countries if the flight
takes 15 hours in all.
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8. Find the distance covered (in km) by a bike in 4 minutes at a speed of 63 km h .
Relative Speed
Relative speed is the speed of one object with respect to another object. There can be two cases of
relative speed:
(a) When two objects are moving in the same direction, then their relative speed is equal to the
difference of their speeds.
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For example, if two bicycles are moving in the same direction with speeds 7 km h and 4 km h ,
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then their relative speed is (7 – 4) km h = 3 km h .
(b) When two objects are moving in the opposite directions, then their relative speed is equal to the
sum of their speeds.
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For example, if two bicycles are moving in the opposite directions with speeds 7 km h and
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4 km h , then their relative speed is (7 + 4) km h = 11 km h .
Example 6: X and Y are two stations 450 km apart. A train starts from X towards Y with a speed of
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75 km h and at the same time another train starts from Y towards X with a speed of
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45 km h . Find the distance from X where they will meet and in how much time.
Solution: Since the trains are moving in opposite directions, relative speed between the trains
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= (75 + 45) km h = 120 km h –1
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Time after which the two trains will meet = Distance = 450 h = 15 = 3 h
Speed 120 4 4
Distance travelled by the first train = Speed × Time
15 1,125
= 75 × km = km = 281.25 km
4 4
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Example 7: A bus leaves from Pune at 8:00 p.m. with a speed of 65 km h . On the same day,
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another bus leaves from Pune at 10:30 a.m. with a speed of 90 km h . Both the buses
are travelling in the same direction. After how many kilometres from Pune will they
meet?
Solution: Difference between starting time of two buses = 10:30 p.m. – 8:00 p.m. = 2.5 hours
\ Distance travelled by first bus due to early departure = (65 × 2.5) km = 162.5 km
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Relative speed of the buses = (90 – 65) km h = 25 km
162.5
Time required to meet each other = h = 6.5 h
25
Required distance from Pune = (6.5 × 90) km = 585 km

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