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?

Explanation:-

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,

Time taken by the faster Boat / Time taken by the Slower boat Upstream = 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