Question

The distance between 2 spots A and B on the same bank of river is 75 km. Speed of the boat in still water is twice as much as that of the speed of the water current of river. The boat travels in the river from A to B and returns back to the spot in 16 hr. What is the speed of the boat in still water ? Plz say answer and explanation.
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Answer 1

Answer:

Explanation:

a good but easy question. so to solve this we must have a idea what happens there at down stream and up stream . in down stream the river helps the boat to reach its destination faster by adding its speed with the boat's one ( like opportunities) . so resultant speed would be addition of the speeds of boat and stream . and at up one river tries to protest the boat by redusing its velocity ( like obstacles) . now , let us assume that speed if stream is x( an old language),. So( sped of boat is p)

( P+x)× t1=l……. 1

(P-x)×t2=l…….2

Deciding 1/2 we get ,

P+x/p-x= t2/t1…..3

By solving these we get, p=(t1+t2)x)/t2-t1. So , l=p+x. So l/p=1+x/p=1+(t2-t1)/t1+t2. This is the required time ( l/p= t3). Hope this will help. Best of luck.

Answer 2

Speed of boat in still water =  12.5 km/hr.

Given:

The distance between 2 spots A and B on the same bank of river is 75 km.

Speed of the boat in still water is twice as much as that of the speed of the water current of river

The boat travels in the river from A to B and returns back to the spot in 16hr

To find:

The speed of boat in still water

Solution:

The distance between the spots A and B = 75km

Speed of boat in still water = 2*(speed of water current of river)

Time taken by boat to travel from A to B and return back = 16hrs

Speed of boat in still water = x km/hr

speed of river = y km/hr

Given, X = 2*Y

⇒ time = distance/speed

⇒ 16 = $\frac{75}{x+y} + \frac{75}{x-y}$

16(x+y)(x-y) = 75 + 75

16($x^{2}- xy +xy -y^{2}$) = 150

16($x^{2} + y^{2}$) = 150

16($2y^{2} + y^{2}$) = 150

16(3y^2) = 150

58y^2 = 150

From this we get x =  12.5 km/hr.

∴ The speed of boat in still water is 12.5km/hr.

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