Question

A boat covers 36 km downstream in 3 hours and the same distance upstream in 4.5 hours. The speed of the boat in still water is:

• A. 8 km/h
• B. 9 km/h
• C. 10 km/h
• D. 11 km/h

Hint:

To remember this concept visually: the speed in still water sits exactly halfway between your downstream and upstream speeds! $$\text{Upstream (8)} \xrightarrow{\quad +2 \quad} \mathbf{\text{Still Water (10)}} \xrightarrow{\quad +2 \quad} \text{Downstream (12)}$$ The moment you find $12$ and $8$, look for the perfect midpoint number in the options. The midpoint is $10$, which also reveals that the speed of the river current is exactly $2 \text{ km/h}$.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
When a boat moves in water, its effective speed depends on the direction of the water current. Moving downstream means traveling in the exact same direction as the stream, causing the water's velocity to boost the boat's speed. Moving upstream means traveling against the flow, which resists the boat's motion and reduces its effective speed.

Step 2: Key Formula or Approach:
1. $\text{Speed} = \frac{\text{Distance}}{\text{Time}}$
2. $\text{Downstream Speed } (D) = u + v$
3. $\text{Upstream Speed } (U) = u - v$
where $u$ is the speed of the boat in still water and $v$ is the speed of the stream. 4. By solving these simultaneous equations, the speed of the boat in still water can be found directly using: $$u = \frac{D + U}{2}$$

Step 3: Detailed Explanation:
Let's calculate the two directional speeds from the given data: Downstream Speed ($D$): The boat travels $36 \text{ km}$ in $3 \text{ hours}$. $$D = \frac{36 \text{ km}}{3 \text{ hours}} = 12 \text{ km/h}$$ Upstream Speed ($U$): The boat travels the same distance ($36 \text{ km}$) in $4.5 \text{ hours}$. $$U = \frac{36 \text{ km}}{4.5 \text{ hours}} = \frac{36}{\left(\frac{9}{2}\right)} = \frac{36 \times 2}{9} = 4 \times 2 = 8 \text{ km/h}$$ Speed of the Boat in Still Water ($u$): Take the average of the downstream and upstream speeds to isolate the boat's independent speed: $$u = \frac{D + U}{2}$$ $$u = \frac{12 + 8}{2} = \frac{20}{2} = 10 \text{ km/h}$$

Step 4: Final Answer:
The speed of the boat in still water is 10 km/h.