Final answer:
The speed of the current is calculated by comparing the speed of a boat going upstream and downstream. After converting the boat's speed to the same units, and solving for the boat's speed in still water and the current speed, we find that the current's speed is 9/50 km/min.
Step-by-step explanation:
The question involves calculating the speed of the current when given the speed of a boat upstream and downstream. The speed of the boat upstream (against the current) is 1 km in 25 minutes, which is 60/25 km/h, and the speed of the boat downstream (with the current) is 1 km in 12 minutes, which is 60/12 km/h. The speed of the current is the difference between boat's speed in still water and its speed upstream or downstream divided by 2.
First, convert the times to hours to match the units:
- Upstream speed: (60/25) × (1/60) km/min = 2.4 km/h
- Downstream speed: (60/12) × (1/60) km/min = 5 km/h
Let's denote the speed of the boat in still water as B and the speed of the current as C. We then have:
- Upstream = B - C = 2.4 km/h
- Downstream = B + C = 5 km/h
By adding these two equations, we get:
2B = 7.4 km/h
So, B = 3.7 km/h (speed of the boat in still water). To find C:
C = 5 km/h - B = 5 km/h - 3.7 km/h = 1.3 km/h
Since the question asks for the speed in km/min, convert this to minutes:
Speed of the current (C): 1.3 km/h × (1/60) = 0.0217 km/min or approximately 9/50 km/min.