Question

the current in a stream moves at a speed of 3km/h. A boat travels 45km upstream and 45km downstream in a total time of 8 hours. What is the speed of the boat in still water?

Answer 1

Alright, so now we can form an equation for total time.

What is the total time taken to go upstream?
Well, we know that \[Time = \frac{Distance}{Speed}\]
Distance the man travels = 45 km
Speed = (x - 3) km/h
Total time to go Upstream = \[Upstream_{time} = \frac{45}{x-3} hours\]
Why is the speed to go upstream (x-3)?
Well, the water always goes downstream, so the water obstructs the boat's motion upstream. So, while going upstream, it take the man more time, which can be seen because the speed is reduced.

Now, what is the total time to go downstream?
Distance travled again = 45 km
Speed = (x+3)km/h
Total time to go downstream = \[Downstream_{time} = \frac{45}{x+3}hours\]
Why is the speed to go downstream (x+3)?
The man is going down now. The river supports the boat in its descent, so it goes downwards with more speed thereby reducing the time it takes to cover the distance.

Total time = \[\frac{45}{(x-3)} + \frac{45}{(x+3)} = 8\]

Solve this equation, you'll get the original speed with no river current.

Understood this? :)