A boat moving upstream takes 8 hours 48 minutes to cover a distance while it takes 4 hours to return to the
starting point, downstream. What is the ratio of the speed of boat in still water to that of water current?

Let the speed of the boat upstream be u kmph and that of downstream be d kmph

Time for upstream = 8 hrs 48 min = $$8\frac{4}{8}$$hrs

Time for downstream = 4 hrs

Distance in both the cases is same.

=>$$u\times8\frac{4}{8}$$= $$d\times 4$$

=> $$\frac{44u}{5} = 4q$$

=> d = $$\frac{11u}{5}$$

Now, the required ratio of Speed of boat : Speed of water current

= $$\frac{speed of upstream + speed of downstream}{2}$$ :

$$\frac{speed of upstream - speed of downstream}{2}$$

=> $$({\frac11u}{5} + u)\div 2 : ({\frac11u}{5} - u)\div 2$$

=> 8 : 3