Final Answer:
The speed of the current is 1 mph.
Step-by-step explanation:
We are given that a boat takes 57 minutes to travel up and down a river. Let's assume that the distance between the two points is d miles. Since the one-way trip is 6 miles, the total distance traveled by the boat is 2d miles. We can use the formula:
time = distance / speed
to relate the time, distance, and speed of the boat. Since the boat's speed in still water is 13 mph, we can write:
57/60 = 2d / (13 + c) + 2d / (13 - c)
where c is the speed of the current. Simplifying this equation, we get:
19/20 = d(13^2 - c^2) / (169 - c^2)
Multiplying both sides by (169 - c^2), we get:
19(169 - c^2) / 20 = d(13^2 - c^2)
Simplifying this equation, we get:
2473 - 19c^2 = 169d
Since the one-way trip is 6 miles, we have:
d = 6
Substituting this value in the above equation, we get:
2473 - 19c^2 = 1014
Solving for c, we get:
c = 1
Therefore, the speed of the current is 1 mph.