Question

A boat can go three-quarter of a kilometer upstream in 11 minutes 15 seconds and also cover the same distance downstream in 7 minutes 30 seconds. The speed of the boat in still water is:

• A. 2 km/h
• B. 3 km/h
• C. 4 km/h
• D. 5 km/h

Hint:

To find the speed of the boat in still water, use the relationship between time, speed, and distance. For upstream, the speed is \( b - s \), and for downstream, the speed is \( b + s \).

Answer 1

The Correct Option is D

Let the speed of the boat in still water be \( b \) km/h and the speed of the stream be \( s \) km/h. The time taken for the boat to go upstream is given by: \[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{0.75}{b - s} \quad \text{hours}. \] The time taken for the boat to go downstream is: \[ \text{Time} = \frac{0.75}{b + s} \quad \text{hours}. \] We are given that the time for upstream is 11 minutes 15 seconds, which is \( \frac{11.25}{60} \) hours, and the time for downstream is 7 minutes 30 seconds, which is \( \frac{7.5}{60} \) hours. Thus, we have the system of equations: \[ \frac{0.75}{b - s} = \frac{11.25}{60}, \quad \frac{0.75}{b + s} = \frac{7.5}{60}. \] Solving these equations, we get the value of \( b = 5 \) km/h. Therefore, the speed of the boat in still water is 5 km/h, which corresponds to option (4).