A boat travels 60 km upstream and back again in 8 hours. If the speed of the boat is 16 km/h, what is the speed of the current?
Let the speed of the boat be x km/h
60/(16+x( + 60/(16-x) = 5
hint: multiply each term by (16+x)(16-x)
(I got x=8)
To find the speed of the current, we can set up a system of equations.
Let's denote the speed of the current as 'c' km/h.
When the boat is traveling upstream, it moves against the current, so its effective speed is the difference between the boat's speed and the speed of the current:
Speed upstream = Boat's speed - Current's speed = 16 - c km/h
Similarly, when the boat is traveling downstream, it moves with the current, so its effective speed is the sum of the boat's speed and the speed of the current:
Speed downstream = Boat's speed + Current's speed = 16 + c km/h
We are given that the boat travels 60 km upstream and back in a total of 8 hours. The time taken to travel 60 km upstream plus the time taken to travel 60 km downstream equals 8 hours:
Time upstream + Time downstream = 8 hours
The time taken to travel a certain distance is equal to distance divided by speed:
60 / (Speed upstream) + 60 / (Speed downstream) = 8
Substituting the expressions we derived earlier for speed upstream and speed downstream:
60 / (16 - c) + 60 / (16 + c) = 8
Now we can simplify and solve this equation to find c, the speed of the current.
Multiply the entire equation by the least common denominator (16 - c)(16 + c):
60(16 + c) + 60(16 - c) = 8(16 - c)(16 + c)
960 + 60c + 960 - 60c = 8(256 - c^2)
1920 = 2048 - 8c^2
Rearrange the equation to isolate c^2:
8c^2 = 2048 - 1920
8c^2 = 128
Divide both sides by 8:
c^2 = 16
Take the square root of both sides:
c = ±√16
Therefore, the speed of the current can be either +4 km/h or -4 km/h.
However, since the question asks for the speed of the current, which is a magnitude, we take the positive value:
The speed of the current is 4 km/h.