Two boats go downstream from point X to Y. The faster boat covers the distance from X to Y, 1.5 times as fast as slower boat. It is known that for every hour slower boat lags behinds the faster boat by 8 km. however, if they go upstream, then the faster boat covers the distance from Y to X in half the time as the slower boat. Find the speed of the faster boat in still water?

Solution(By Examveda Team)

Given,
Speed of the faster boat Downstream = 1.5 × speed of the slower boat downstream ----------(1) [Difference in First hour]
Speed of the Faster Boat Downstream = Speed of the slower boat + 8 ------------- (2)
Using Equation (1) and (2), we get
Speed of the faster Boat Downstream = 16 kmph
Now,
$$\frac{{{\text{Time taken by the faster Boat}}}}{{{\text{Time taken by the Slower boat Upstream}}}}$$        = $$\frac{1}{2}$$
Hence,
Time taken by the faster Boat Upstream = 2 × Time taken by the slower Boat Upstream . . . . . . . (3)
And,
Faster boat's speed upstream - 8 = Slower boat's speed upstream . . . . . . . . (4) Using (4) and (3), we get
Speed of the faster Boat upstream = 8 kmph
Thus,
Speed of the faster Boat in still water = 20 kmph