Final answer:
The speed of the current is 3.5 miles/hour.
Step-by-step explanation:
To find the speed of the current in this problem, we need to use the formula:
Boat's speed with current - Current's speed = Distance / Time
Given that the boat can travel 76 miles in 2 hours with the current, we have:
Boat's speed with current - Current's speed = 76 miles / 2 hours
Similarly, when traveling against the current, the boat can travel 62 miles in 2 hours. Using the same formula, we get:
Boat's speed against current - Current's speed = 62 miles / 2 hours
We can now set up a system of equations to solve for the speed of the boat and the speed of the current. Let's call the speed of the boat 'b' and the speed of the current 'c':
- b + c = 76/2 = 38 miles/hour
- b - c = 62/2 = 31 miles/hour
Solving this system of equations gives us:
b = 34.5 miles/hour
Therefore, the speed of the current is 38 - 34.5 = 3.5 miles/hour.