In A Stream The Current Flows At The Rate 4 Miles/hr. For A Boat The Time Taken To Cover A Certain Distance Upstream Is 5 Times The Time It Takes To Cover The Same Distance Downstream. Find The Speed Of The Boat In Still Water?

Let the speed of the boat in still water = x miles/hr.
Speed of the boat downstream will be greater than its speed in still water, due to favorable current of water.
\ Speed of the boat downstream = Speed of the boat + Speed of water current.
= (x+4) miles/hr.
Speed of the boat upstream will be less than its speed in still water, due to opposing current of water.
\Speed of the boat upstream = Speed of the boat - Speed of the current.
= (x-40)miles/hr.
Let the time taken to cover the distance downstream = t hrs.
\Time taken to cover distance upstream = 5t hr.
Now, distance traveled downstream = Speed * Time
= (x+4)t miles.
Distance traveled upstream = (x-4)5t miles.
Since distance traveled both ways are same.
(x+4)t = (x-4)5t
Dividing both sides by 't'(¹0).
(x+4) = 5(x-4)
x+4 = 5x-20
Transposing 5x and 4
5x - x = 20 + 4
4x = 24
x = 24/4 = 6