Page 133 - ICSE Math 7

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Example 12: A boat travels with a speed of 17 km h in still water. If the speed of the stream is
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7 km h , find:
(a) the time taken by the boat to go 72 km downstream.
(b) the time taken by the boat to go 40 km upstream.
Solution: (a) Speed of the boat downstream = Speed of the boat in still water + speed of the
–1
stream = (17 + 7) km h = 24 km h –1
Distance 72
Time taken by the boat to go 72 km downstream = = h = 3 h
Speed 24
(b) Speed of the boat upstream = Speed of the boat in still water – speed of the
–1
stream = (17 – 7) km h = 10 km h –1
40
Time taken by the boat to go 40 km upstream = h = 4 h
10
2
3
Example 13: A person driving at of his usual speed takes 2 hours extra to reach a particular
3 4
destination. Find the usual time taken by him.
Solution: If a person drives at half of his usual speed, time required to cover a certain distance
will be double the usual time.
3
2
Similarly, when driving at of the usual speed, time taken will be of the usual time.
2
3
3 3
of the usual time = usual time + 2 h
2 4
3 11 1 11
⇒ – 1 usual time = h ⇒ of usual time = h
2 4 2 4
11 11 1
⇒ usual time = h × 2 = h = 5 h
4 2 2

EXERCISE 11.2

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1. Two people X and Y are 270 m apart. X starts walking towards Y at a speed of 1.5 m s and Y
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starts walking towards X at a speed of 1.2 m s . At what time and at how much distance from
the starting point of X will they meet?
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2. Two cars start from the same point with speeds 39 km h and 51 km h . Find the distance
between them after 15 min, if they travel in:
(a) the same direction (b) the opposite direction

3. A train 190 m long passes a railway platform 250 m long in 22 seconds. Determine:
(a) the speed of the train in km h –1
(b) the time taken by the train to pass a stationary person
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(c) the time taken by the train to pass a man running in the direction of the train at a speed of 10 m s .
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4. The speed of a motor boat in still water is 17.5 km h . If the speed of the stream is 5.5 km h ,
determine:
(a) the time taken by the boat to go 103.5 km downstream

(b) the time taken by the boat to go 39 km upstream
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5. The speed of a boat in still water is 13 km h . If the boat travels 84.7 km downstream in
5.5 hours, find the speed of the stream.

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