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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 +48s−324 =0……(2)  
Evaluate equation (2) by factorization.
  ⇒ s 2 +48s−324=0 ⇒ s 2 +54s−6s−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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