# 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?

May 31, 2016

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

#### Explanation:

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

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

As the two are equal

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

$6 x + 24 = 14 x - 56$

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

Hence $x = 10$.