The time taken by a boat to go to a certain distance against the current is the same as to go the double distance along the current. The speed of the current is 3 km/h. How much time will the boat take to travel 57.6 km in still water?
Question
The time taken by a boat to go to a certain distance against the current is the same as to go the double distance along the current. The speed of the current is 3 km/h. How much time will the boat take to travel 57.6 km in still water?
Solution
Let's denote the speed of the boat in still water as 'b' (in km/h), and the speed of the current as 'c' (in km/h). We know that 'c' is 3 km/h.
The speed of the boat against the current is (b - c) and the speed of the boat along the current is (b + c).
According to the problem, the time taken to travel a certain distance against the current is the same as the time taken to travel double that distance along the current. We know that time = distance/speed, so we can set up the following equation:
Distance/(b - c) = 2*Distance/(b + c)
We can simplify this to:
1/(b - c) = 2/(b + c)
Solving for 'b', we get:
b = 5c
Since we know that 'c' is 3 km/h, 'b' is 15 km/h.
Now, we want to find out how much time the boat will take to travel 57.6 km in still water. Using the formula time = distance/speed, we get:
Time = 57.6 km / 15 km/h = 3.84 hours.
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