Question

a boat can cover 10 km up the stream and 5 km down the stream in 6 hours, if the speed of the stream is 1.5 km/h, find the speed of the boat in still water.

Answer 1

Answer :  

The speed of the boat in still water is 3.5 km/h

SOLUTION IS IN THE ATTACHMENT

Given :  

speed of the stream is 1.5 km/h

Time taken = 6 hours

A boat can cover up the stream = 10 km  

A boat can cover down the stream = 5 km  

Here we have done factorisation by middle term splitting..

Speed of boat cannot be negative so x = -1 cannot be taken

Hence speed of boat in still water is = 3.5 km/hr

Hope this answer will help you ......

Answer 2

3.5 kmph is the speed of the boat.

Given:

The distance covered by the boat up the stream is 10 km

The distance covered by the boat down the stream is 5 km

The time taken in both travels is 6 hours.

The speed of the stream is 1.5 km/h

To find:

Speed of the boat in still water = ?

Solution:

The distance covered by the boat up the stream is 10 km

The distance covered by the boat down the stream is 5 km

The time taken in both travels is 6 hours.

The speed of the stream is 1.5 km/h

Using time = distance/speed, we get the following equation

$\begin{array}{l}{\frac{\text {distance}}{\text {speed}}=\frac{10}{x-1.5}+\frac{5}{x+1.5}=6(\text { time })} \\ {\frac{10}{x-1.5}+\frac{5}{x+1.5}=6} \\ {6 x^{2}-15 x+21} \\ {(2 x-7)(x+1) }\end{array}$

Now with the equation solved we get two values x = 3.5, -1.

Now speed cannot be -1 therefore, the speed of the boat in still water is 3.5 kmph.