Answer:
The average speed of the river's current is 3.5 mph.
Explanation:
If the speedboat is capable of traveling 35 mph in Stillwater, but went 84 mph up the river (i.e., against the current) for 3 hours, then we can use this information to determine the average speed of the river's current.
Let's assume that the speed of the river's current is C, and the speed of the boat in still water is B. When the boat is traveling against the current, its effective speed is reduced by the speed of the river's current, so the boat's speed upstream can be expressed as:
B - C
We know that the boat's speed upstream was 84 mph, so we can set up the following equation:
B - C = 84/3 = 28 mph
We also know that the boat's speed in still water is 35 mph, so we can set up another equation:
B + C = ?
We want to solve for the average speed of the river's current (i.e., C), so we can rearrange the first equation to get B in terms of C:
B = C + 28
Now we can substitute this expression for B into the second equation:
B + C = 35 + C
Substituting B = C + 28 gives:
C + 28 + C = 35 + C
Simplifying this equation gives:
2C + 28 = 35
Subtracting 28 from both sides gives:
2C = 7
Dividing both sides by 2 gives:
C = 3.5 mph
Therefore, the average speed of the river's current is 3.5 mph.