Let the speed of the boat in calm water be $b = 5$ mph, and let the speed of the current be $c$ mph.

When the boat travels upstream, its effective speed is reduced by the speed of the current, so its speed is $b - c = 5 - c$ mph.
When the boat travels downstream, its effective speed is increased by the speed of the current, so its speed is $b + c = 5 + c$ mph.

We are given that the time taken to travel upstream is 3 hours, and the time taken to travel downstream is 2 hours.

Let the distance traveled upstream and downstream be the same, and let that distance be $d$.

We can use the formula for time:
$\text{Time} = \frac{\text{Distance}}{\text{Speed}}$

Thus, for upstream: $\frac{d}{5 - c} = 3$

For downstream: $\frac{d}{5 + c} = 2$

Step 1: Solve for $d$ in both equations

From the upstream equation: $d = 3(5 - c) = 15 - 3c$

From the downstream equation: $d = 2(5 + c) = 10 + 2c$

Step 2: Set the two expressions for $d$ equal to each other:

$15 - 3c = 10 + 2c$

Step 3: Solve for $c$

$15 - 10 = 2c + 3c$ $5 = 5c$ $c = 1$

Final Answer:

The speed of the current is $\boxed{1}$ mph.

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Would you like me to explain any steps in more detail? Or do you have another question?

Additional questions to consider:

1. How would the time change if the current were faster?
2. What would happen if the boat’s speed in calm water were reduced to 4 mph?
3. How can the boat's total round-trip time be calculated for a given current speed?
4. What other real-life factors might affect the boat's speed in the river (e.g., water turbulence)?
5. How would you approach a situation where the boat can only travel a certain distance upstream and then needs to turn back?

Tip: Always check that your distances match when comparing different time formulas.