Final answer:
The speed of the current is found to be 1 mph by setting up an equation based on the times being equal for Maria paddling upstream and downstream, then solving for the current's speed.
Step-by-step explanation:
The question asks us to determine the speed of the current given that Maria can paddle her canoe 2 miles upstream and 6 miles downstream in the same amount of time. She can paddle at a speed of 2 mph in still water. To find the speed of the current, we can use the following approach:
Let the speed of the current be c miles per hour.
When Maria paddles upstream, her effective speed is (2-c) mph.
When she paddles downstream, her effective speed is (2+c) mph.
The time it takes to paddle 2 miles upstream is the distance divided by the effective upstream speed: Time upstream = 2 / (2 - c).
The time it takes to paddle 6 miles downstream is the distance divided by the effective downstream speed: Time downstream = 6 / (2 + c).
Since these times are equal, we have the equation: 2 / (2 - c) = 6 / (2 + c).
Solve for c to find the speed of the current.
Solution Step-by-Step:
1. Write the equation from equal times: 2/(2 - c) = 6/(2 + c).
2. Cross-multiply to clear the denominators: 4 + 2c = 12 - 6c.
3. Collect like terms: 2c + 6c = 12 - 4.
4. Combine like terms: 8c = 8.
5. Solve for c: c = 1 mph.
Therefore, the speed of the current is 1 mph.