A boat covers a certain distance against the stream in 9 hours 36 min and it covers the same distance along the stream in 6 hours. What is the ratio of the speed of the boat in still water to that of the stream?

13 : 3

Ratio of time = 576 : 360

=  8 : 5

As distance is same so the speed is inversely proportional to time.

So ,  Ratio of speed = 5 : 8

Let upstream speed = 5R

downstream speed =  8R

We know ,

Speed of boat = \(\frac{Upstream \; speed \;+ Downstream \;speed}{2}\)

Spped of Stream = \(\frac{Downstream \; speed \;+ Upstream \;speed}{2}\)

From here speed of boat = \(\frac{8R+ 5R}{2}\)= \(\frac{13R}{2}\)

And speed of stream = \(\frac{8R - 5R}{2}\) = \(\frac{3R}{2}\)

Hence , Required ratio will be  = 13 : 3