Q:

What is the ratio between the speed of the boat and speed of the water current?

A boat running upstream takes 8 hours 48 minutes to cover a certain distance, while it takes 4 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively?
A.  $2 : 1$    
B.  $3 : 2$
C.  $8 : 3$    
D.  Cannot be determined
E.  None of these
What I think can be useful, they travel the same distance, so we can equate them taking up down speeds as x and y, but then what?
Also, how are these types of question solved quickly?  

A:

Denote with $x$ the speed of the boat and with $y$ the speed of the water current. Then it is given that when the boat travels upstream with a speed of $x-y$ it covers a certain distance, say $D$, in $8$h and $48$m or equivalently in $528$ minutes. Accordingly, when the boat travels downstream with a speed of $x+y$ it covers the same distance $D$ in $4$h or equivalently in $240$ minutes. Thus $$D=528(x-y)$$ as well as $$D=240(x+y)$$
Equating the right sides you have $$528(x-y)=240(x+y)$$ which gives $$288x=768y$$ By dividing both sides with $96$ the last equation reduces to $$3x=8y$$ so that the correct answer is C.

