Shortcut Trick
Speed of Boat A in still water (uA) = 15 km/hr
Speed of Boat B in still water (uB) = 40% of (2 × 15) = 12 km/hr
When one boat travels upstream and the other travels downstream, the relative speed of the boats is simply the sum of their speeds in still water, because the stream speed (v) cancels out: (uA − v) + (uB + v) = uA + uB = 15 + 12 = 27 km/hr
Meeting time = Distance ÷ Relative Speed = 108 ÷ 27 = 4 hours
∴ The correct answer is 4 hours.
Alternate Method
Given:
Speed of boat A in still water (uA) = 15 km/hr
Speed of boat B in still water (uB) = 40% of (2 × 15) = 0.40 × 30 = 12 km/hr
Total distance between boats = 108 km
Let the speed of the stream be v km/hr.
Formula Used:
Upstream speed of Boat A = uA − v = 15 − v
Downstream speed of Boat B = uB + v = 12 + v
Relative speed = Speed of A + Speed of B
Time to meet = Total Distance ÷ Relative Speed
Calculations:
⇒ Relative Speed = (15 − v) + (12 + v)
⇒ Relative Speed = 15 + 12 = 27 km/hr
⇒ Time to meet = 108 ÷ 27
⇒ Time to meet = 4 hours
∴ The correct answer is 4 hours.
Additional Information
Relative Speed in Rivers
When two boats move towards each other, one going upstream and the other going downstream, the effect of the stream speed cancels out completely. The relative speed is simply the sum of their individual speeds in still water (u1 + u2).
Upstream and Downstream Formulas
Downstream speed (D) = u + v and Upstream speed (U) = u − v, where u is the speed of the boat in still water and v is the speed of the stream.
Finding Boat and Stream Speeds
Speed of boat in still water u = (D + U) ÷ 2, and Speed of stream v = (D − U) ÷ 2.