a boat crosses a .2mi river is heading perpendicularly relative to the shore. its speed in still water is 4mph and the speed of the current is 6mph
To find the time it takes for the boat to cross a 0.2-mile wide river heading perpendicularly to the shore, we can use the formula:
Time = Distance / Speed
The boat has two velocities: its speed in still water (4 mph) and the speed of the current (6 mph). When the boat is moving against the current, its effective speed is reduced. When it is moving along with the current, its effective speed increases.
Let's break down the different parts of the boat's motion:
1. Crossing the river against the current:
The boat is moving perpendicularly to the shore, so the distance it has to cross is the width of the river, which is 0.2 miles. To calculate the boat's effective speed, we subtract the current's speed from the boat speed:
Effective speed = Boat speed - Current speed = 4 mph - 6 mph = -2 mph (negative because it's moving against the current).
Now we can calculate the time taken:
Time = Distance / Speed = 0.2 miles / (-2 mph) = -0.1 hours (convert miles to hours by dividing by speed).
2. Returning across the river along with the current:
Since the boat is now moving along with the current, its effective speed increases. We add the current's speed to the boat speed to find the effective speed:
Effective speed = Boat speed + Current speed = 4 mph + 6 mph = 10 mph.
The distance is still 0.2 miles, so we can calculate the time:
Time = Distance / Speed = 0.2 miles / 10 mph = 0.02 hours.
To find the total time, we add the time for each segment:
Total time = Time crossing against the current + Time crossing along with the current
Total time = -0.1 hours + 0.02 hours = -0.08 hours.
Since time cannot be negative, it means that the boat took 0.08 hours (or 4.8 minutes) to cross the river.