Question

Motor boat takes 12 hours to go downstream and it takes 24 hours to return  the same distance. What is the time taken by  boat in still water?

Answer 1

at last x is distance between A and B . and a is speed of boat . as we know x/a will give time taken to cover AB by boat in still water

Answer 2

Given that,

Time taken by the motorboat to go downstream is 12 hours while 24 hours to return the same distance.

To find,

The time taken by boat in still water.

Solution,

Let D is the total distance. The speed of the boat be x km/h and the speed of steam be y km/h.

According to given condition, we have,

$x+y=\dfrac{D}{12}\ .......(1)$

and

$x-y=\dfrac{D}{24}\ .......(2)$

Adding equation (1) and (2) we get :

$x+y+x-y=\dfrac{D}{12}+\dfrac{D}{24}\\\\2x=\dfrac{D}{12}+\dfrac{D}{24}\\\\2x=\dfrac{D}{8}\\\\x=\dfrac{D}{16}\ ....(3)$

Since, $v=\dfrac{d}{t}$

For boat,

$x=\dfrac{D}{T}$ .....(4)

T is time taken by boat in still water

From equation (3) and (4) we have,

$\dfrac{D}{16}=\dfrac{D}{T}\\\\T=16\ h$

So, the time taken by the boat in still water is 16 hours.

Learn more,

Speed

https://brainly.in/question/6152860