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Q.

A motorboat whose speed in still water is 18 km/h takes 1 hour more to go 24 km upstream that to return downstream to the same spot. Find the speed of the stream.

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a

6km/h

b

12km/h

c

18km/h

d

20km/h

answer is A.

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Detailed Solution

Given that a motorboat whose speed in still water is 18 km/h takes 1 hour more to go 24 km upstream that to return downstream to the same spot.
Solving this question requires the knowledge of these concepts Speed of boat upstream = Speed of boat in still water - speed of stream.
Speed of boat downstream = Speed of boat in still water + speed of stream.
Time (T) taken by a body to cover a distance (D) at a speed(S) is given by the ratio

f the distance to the speed . That is T = D S .

Form an equation using the given information using the formula T = D S .

Hence, Speed of boat upstream = 18 – s
Speed of boat downstream = 18 + s

⇒ 24 18 − s = 24 18 + s + 1

Form a quadratic equation by simplifying equation (1).

⇒ 24 18 − s = 24 18 + s + 1 ⇒ 24 18 − s = 42 + s 18 + s ⇒ 24 (18 + s) = (18 − s) (42 − s) ⇒ s 2 + 48 s − 324 = 0 … … (2)

Evaluate equation (2) by factorization.

⇒ s 2 + 48 s − 324 = 0 ⇒ s 2 + 54 s − 6 s − 324 = 0 ⇒ s (s + 54) − 6 (s + 54) = 0 ⇒ (s + 54) (s − 6) = 0

Hence, as speed can’t be negative reject the value -54.
So, the calculated speed of the stream = 6 km/h.
Therefore, the correct option is 1.

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A motorboat whose speed in still water is 18 km/h takes 1 hour more to go 24 km upstream that to return downstream to the same spot. Find the speed of the stream.