Question

A person rows a boat 10 kms along the stream in 30 minutes and returns to the starting point in 40 minutes. The speed of the stream is:

• A. 17.5 km/h
• B. 2.5 km/h
• C. 5 km/h
• D. 15 km/h

Hint:

Remember these two key formulas: Speed of stream = (Downstream Speed - Upstream Speed) / 2 Speed of boat in still water = (Downstream Speed + Upstream Speed) / 2 These can save a lot of time in boat and stream problems.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
This problem involves relative speed in the context of boats and streams.
Downstream speed (\(S_D\)): Speed of boat in still water (\(S_B\)) + Speed of stream (\(S_S\)).
Upstream speed (\(S_U\)): Speed of boat in still water (\(S_B\)) - Speed of stream (\(S_S\)).
Speed of stream (\(S_S\)) = \( \frac{S_D - S_U}{2} \).
Step 2: Key Formula or Approach:
1. Calculate the downstream speed (\(S_D\)). 2. Calculate the upstream speed (\(S_U\)). 3. Use the formula to find the speed of the stream. Remember to convert time from minutes to hours.
Step 3: Detailed Explanation:
Downstream journey (along the stream):
Distance = 10 km.
Time = 30 minutes = \( \frac{30}{60} \) hours = 0.5 hours.
Downstream speed (\(S_D\)) = \( \frac{\text{Distance}}{\text{Time}} = \frac{10}{0.5} = 20 \) km/h.
Upstream journey (returning):
Distance = 10 km.
Time = 40 minutes = \( \frac{40}{60} \) hours = \( \frac{2}{3} \) hours.
Upstream speed (\(S_U\)) = \( \frac{\text{Distance}}{\text{Time}} = \frac{10}{2/3} = 10 \times \frac{3}{2} = 15 \) km/h.
Calculate the speed of the stream:
Speed of stream (\(S_S\)) = \( \frac{S_D - S_U}{2} \)
\(S_S = \frac{20 - 15}{2} = \frac{5}{2} = 2.5 \) km/h.
Step 4: Final Answer:
The speed of the stream is 2.5 km/h.