Question

A man takes 24 minutes to row 10 km upstream, which is one-fifth more than the time he takes on his way downstream. What is his speed of rowing in still water?

• A. 27.5 km/hr
• B. 25.5 km/hr
• C. 24 km/hr
• D. 22.5 km/hr

Hint:

When solving problems involving relative speed and time, carefully set up equations based on the relationship between time, speed, and distance. Use the concept of relative speed for upstream and downstream problems.

Answer 1

The Correct Option is A

Step 1: Define variables.
Let the speed of rowing in still water be \( x \) km/hr, and the speed of the current be \( y \) km/hr.
- Speed upstream = \( x - y \) km/hr
- Speed downstream = \( x + y \) km/hr Step 2: Time taken for upstream and downstream.
The time taken to row upstream is given as 24 minutes, which is \( \frac{24}{60} = \frac{2}{5} \) hours. The distance is 10 km, so: \[ \text{Time upstream} = \frac{10}{x - y} = \frac{2}{5} \text{ hours}. \] The time taken to row downstream is \( \frac{1}{5} \) less than the time taken upstream. Thus: \[ \text{Time downstream} = \frac{10}{x + y} = \frac{2}{5} - \frac{1}{5} = \frac{1}{5} \text{ hours}. \] Step 3: Set up equations.
From the time formulas, we can set up two equations: \[ \frac{10}{x - y} = \frac{2}{5} \quad \text{(1)} \] \[ \frac{10}{x + y} = \frac{1}{5} \quad \text{(2)} \] Step 4: Solve the system of equations.
From equation (1): \[ x - y = \frac{10}{\frac{2}{5}} = 25 \] From equation (2): \[ x + y = \frac{10}{\frac{1}{5}} = 50 \] Now, solve these two equations: \[ x - y = 25 \quad \text{(3)} \] \[ x + y = 50 \quad \text{(4)} \] Add equations (3) and (4): \[ (x - y) + (x + y) = 25 + 50 \] \[ 2x = 75 \] \[ x = \frac{75}{2} = 37.5 \, \text{km/hr}. \] Thus, the speed of rowing in still water is \( 37.5 \, \text{km/hr} \). Step 5: Conclusion.
The correct speed of rowing in still water is \( \boxed{37.5} \, \text{km/hr} \), which corresponds to option (1).