Final answer:
To find the speed of the current, we can use the concept of relative velocity and solve an equation. When going upstream, the boat's speed relative to the ground is 17 - c mph. When returning downstream, the boat's speed relative to the ground is 17 + c mph. The total time for the trip is 8.5 hours.
Step-by-step explanation:
To find the speed of the current, we can use the concept of relative velocity. Let's assume the speed of the current is 'c'. The boat's speed relative to the water is 17 mph and the total time for the trip is 8.5 hours.
When going upstream, the boat's speed relative to the ground is 17 - c mph. The distance traveled upstream is 52 miles. So, the time taken for the upstream journey is 52/(17-c) hours.
When returning downstream, the boat's speed relative to the ground is 17 + c mph. The distance traveled downstream is also 52 miles. So, the time taken for the downstream journey is 52/(17+c) hours.
According to the given information, the total time for the trip is 8.5 hours. Therefore, we can write the equation: 52/(17-c) + 52/(17+c) = 8.5.
Solving this equation will give us the value of 'c', which is the speed of the current.