The speed of a stream is 4 mph. A boat travels 6 miles upstream in the same time it takes to travel 14 miles downstream. What is the speed of the boat in still water?

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The speed of a stream is 4 mph. A boat travels 6 miles upstream in the same time it takes to travel 14 miles downstream. What is the speed of the boat in still water?

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Answer 1 · 2016-05-31T12:22:22

The speed of boat in still water be $10$ $10$ $m p h$ $mph$ .

Explanation:

Let the speed of boat in still water be $x$ $x$ mph. AS, the speed of stream is $4$ $4$ mph, upstream speed will be $(x - 4)$ $(x-4)$ and downstream speed will be $(x + 4)$ $(x+4)$ .

Time taken by boat for travelling $6$ $6$ miles upstream will be $\frac{6}{x - 4}$ $6/(x-4)$ and time taken by boat for travelling $14$ $14$ miles downstream is $\frac{14}{x + 4}$ $14/(x+4)$ .

As the two are equal

$\frac{6}{x - 4} = \frac{14}{x + 4}$ $6/(x-4)=14/(x+4)$ or $6 (x + 4) = 14 (x - 4)$ $6(x+4)=14(x-4)$ or

$6 x + 24 = 14 x - 56$ $6x+24=14x-56$

Hence $14 x - 6 x = 24 + 56 = 80$ $14x-6x=24+56=80$ or $8 x = 80$ $8x=80$ .

Hence $x = 10$ $x=10$ .

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The speed of a stream is 4 mph. A boat travels 6 miles upstream in the same time it takes to travel 14 miles downstream. What is the speed of the boat in still water?

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