A boat takes 18 minutes to go 59.4 km upstream. The ratio of the speed of the boat in still water to that of the stream is 3 : 2. How much total time (in hours) will the boat take to go 29.3 km upstream and 51.5 km downstream?​

Correct option is D

Given:

Time taken by the boat to go 59.4 km upstream = 18 minutes
Ratio of the speed of the boat in still water to the speed of the stream = 3:2
Distance to go upstream = 29.3 km
Distance to go downstream = 51.5 km

Concept Used:

Speed = Distance / Time
Speed of the boat in still water = b km/hr
Speed of the stream = s km/hr
Upstream speed = b - s
Downstream speed = b + s

Solution:

Find the speed of the boat and the stream.
We are given that the ratio of the speed of the boat in still water to the speed of the stream is 3:2, so let:
Speed of the boat in still water = 3x km/hr
Speed of the stream = 2x km/hr

Find the time taken to travel 59.4 km upstream:
The speed of the boat upstream is the speed of the boat in still water minus the speed of the stream:
Upstream speed = 3x - 2x = x km/hr
The boat takes 18 minutes = 0.3 hours to travel 59.4 km upstream, so:
Upstream speed = 59.4 / 0.3 = 198 km/hr
Thus, x = 198.

Find the speed of the boat and the stream:
Speed of the boat in still water = 3x = 3 * 198 = 594 km/hr
Speed of the stream = 2x = 2 * 198 = 396 km/hr

Calculate the time taken to travel 29.3 km upstream:
Upstream speed = 594 - 396 = 198 km/hr
Time upstream = 29.3 / 198 = 0.148 hours

Calculate the time taken to travel 51.5 km downstream:
Downstream speed = 594 + 396 = 990 km/hr
Time downstream = 51.5 / 990 = 0.052 hours
 Find the total time taken:
Total time = 0.148 + 0.052 = 0.2 hours