boat which has a speed of 5 km/hr in still water crosses a river of width 1 km along the shortest possible path in 15 minutes. Then what is the velocity of the river water in km/hr ?
Question
boat which has a speed of 5 km/hr in still water crosses a river of width 1 km along the shortest possible path in 15 minutes. Then what is the velocity of the river water in km/hr ?
Solution
Step 1: Convert the time taken to cross the river into hours. Since 15 minutes is 0.25 hours.
Step 2: Calculate the actual speed of the boat during the crossing. The boat crosses a 1 km wide river in 0.25 hours, so its speed is Distance/Time = 1km / 0.25hr = 4 km/hr.
Step 3: The speed of the boat in still water is given as 5 km/hr. The actual speed of the boat is less because it is moving against the current.
Step 4: Subtract the actual speed of the boat from its speed in still water to find the speed of the river current. So, 5 km/hr - 4 km/hr = 1 km/hr.
Therefore, the velocity of the river water is 1 km/hr.
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