A boat takes 2.70 hours to travel 40.0 km down a river, then 5.90 hours to return. How fast is the river flowing?
To determine the speed of the river, we need to first understand how the boat's speed is affected by the river's current.
Let's assume the speed of the boat in still water is "B" km/h, and the speed of the river's current is "R" km/h.
When the boat is traveling downstream (i.e., with the current), it benefits from the additional speed provided by the river's current. Therefore, the effective speed of the boat is the sum of the boat's speed in still water and the speed of the current.
On the other hand, when the boat is traveling upstream (i.e., against the current), it has to overcome the opposing force of the current, which reduces its effective speed. Therefore, the effective speed of the boat is the difference between the boat's speed in still water and the speed of the current.
Let's use this information to solve the problem.
Given:
Time taken downstream (with the current): 2.70 hours
Time taken upstream (against the current): 5.90 hours
Distance traveled in both directions: 40.0 km
Let's calculate the effective speed of the boat when traveling downstream:
Effective speed downstream = Boat speed in still water + River current speed
The formula for calculating speed is distance divided by time:
Effective speed downstream = 40.0 km / 2.70 hours
Now, let's calculate the effective speed of the boat when traveling upstream:
Effective speed upstream = Boat speed in still water - River current speed
Effective speed upstream = 40.0 km / 5.90 hours
Now, we have two equations:
1. B + R = 40.0 km / 2.70 hours
2. B - R = 40.0 km / 5.90 hours
We can solve these equations simultaneously to find the values of B (boat's speed in still water) and R (river current speed).
By adding both equations, we can eliminate the variable R:
(B + R) + (B - R) = 40.0 km / 2.70 hours + 40.0 km / 5.90 hours
2B = 14.8148 km/h
B = 7.4074 km/h
Now we substitute the value of B back into one of the original equations to find the value of R:
7.4074 km/h + R = 40.0 km / 2.70 hours
R = 40.0 km / 2.70 hours - 7.4074 km/h
R ≈ 2.22 km/h
Therefore, the speed of the river is approximately 2.22 km/h.