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  • A boat takes 4 hours to travel a certain distance upstream and 3 hours to cover the same distance downstream. If the speed of the stream is 2 km/h, what is the speed of the boat in still

A boat takes 4 hours to travel a certain distance upstream and 3 hours to cover the same distance downstream. If the speed of the stream is 2 km/h, what is the speed of the boat in still water?

Option: 1

8 km/h


Option: 2

10 km/h


Option: 3

12 km/h

 


Option: 4

14 km/h


Answers (1)

best_answer

Let the speed of the boat in still water be denoted by "b" (in km/h) 

and the distance of the journey is denoted by "d" (in km).

Since the boat is travelling upstream against the current, its effective speed will be reduced by the speed of the current, which is 2 km/h. Therefore, the speed of the boat upstream will be (b - 2) km/h.

Similarly, when travelling downstream with the current, the effective speed of the boat will be increased by the speed of the current, making it (b + 2) km/h.

We know that the time taken to travel upstream is 4 hours and the time taken to travel downstream is 3 hours. Therefore, we can use the formula:

\mathrm{ time=\frac{distance}{speed}}

For the upstream journey, we have:

    \mathrm{ 4=\frac{d}{(b-2)}}

For the downstream journey, we have:

\mathrm{ 3=\frac{d}{(b+2)}}

Solving for d in both equations gives:

\\\mathrm{d=4b-2}\\ \\\mathrm{ d=3b+2}

Setting these two expressions for d equal to each other and solving for b, we get:

\mathrm{ 4(b-2) = 3(b+2)}

\mathrm{4b-8 = 3b+6}

\mathrm{b=14}

Therefore, the speed of the boat in still water is 14km/h.

Posted by

himanshu.meshram

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