The difference between the downstream speed and the upstream speed of a boat is 10 kmph. If the boat can cover 70 km downstream in 3 hours 30 minutes, what is the speed of the boat in still water? (in kmph)

Options

A. 15
B. 20
C. 25
D. 10

Answer

To solve the problem, we need to find the speed of the boat in still water. Let's denote:

- Speed of the boat in still water = \( b \) kmph
- Speed of the current (stream) = \( c \) kmph

From the problem, we know:

1. The difference between the downstream speed and the upstream speed is 10 kmph:
\[ (b + c) - (b - c) = 10 \]
Simplifying this gives:
\[ 2c = 10 \implies c = 5 \text{ kmph} \]

2. The boat covers 70 km downstream in 3 hours and 30 minutes. First, we convert 3 hours and 30 minutes into hours:
\[ 3 \text{ hours } 30 \text{ minutes} = 3.5 \text{ hours} \]

3. The downstream speed can be calculated using the formula:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{70 \text{ km}}{3.5 \text{ hours}} = 20 \text{ kmph} \]

4. Now, we can set up the equation for the downstream speed:
\[ b + c = 20 \]
Substituting \( c = 5 \) into the equation gives:
\[ b + 5 = 20 \]

5. Solving for \( b \):
\[ b = 20 - 5 = 15 \text{ kmph} \]

Thus, the speed of the boat in still water is \( 15 \) kmph.