A boat goes 30 km downstream in 2 hours and returns upstream in 3 hours. What is the speed of the boat in still water?
Quantitative AptitudeTime Speed Distance AI confidence: 98%Asked 8/5/2026
AI-Verified Answer
Prabhakar, let us solve this carefully step by step.
Given Data
- Distance downstream \(= 30 \text{ km}\)
- Time taken downstream \(= 2 \text{ hours}\)
- Distance upstream \(= 30 \text{ km}\)
- Time taken upstream \(= 3 \text{ hours}\)
Relevant Concept
Speed means the distance travelled in unit time. It is given by the formula:
\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}}
\]
In problems of boats and streams:
- Downstream speed \(=\) speed of boat in still water \(+\) speed of stream
- Upstream speed \(=\) speed of boat in still water \(-\) speed of stream
This applies because when the boat moves downstream, the current of water helps the boat, and when it moves upstream, the current opposes the boat.
Solution
Step 1: Find the downstream speed
\[
\text{Downstream speed} = \frac{30}{2} = 15 \text{ km/h}
\]
Step 2: Find the upstream speed
\[
\text{Upstream speed} = \frac{30}{3} = 10 \text{ km/h}
\]
Step 3: Use the formula for speed in still water
Let the speed of the boat in still water be \(b\) km/h and the speed of the stream be \(s\) km/h.
\[
b + s = 15
\]
\[
b - s = 10
\]
Add the two equations:
\[
(b+s) + (b-s) = 15 + 10
\]
\[
2b = 25
\]
\[
b = \frac{25}{2} = 12.5
\]
Final Answer
Therefore, the speed of the boat in still water is
\[
\boxed{12.5 \text{ km/h}}
\]
Summary of Key Points
- Downstream speed \(= \frac{30}{2} = 15 \text{ km/h}\)
- Upstream speed \(= \frac{30}{3} = 10 \text{ km/h}\)
- Speed of boat in still water \(= \frac{\text{downstream speed} + \text{upstream speed}}{2}\)
- So, speed in still water \(= \frac{15+10}{2} = 12.5 \text{ km/h}\)
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