Final answer:
The time it takes to travel a fixed distance varies inversely with the speed traveled. Given that Carson takes 60 minutes to bike 5 miles, we can use inverse variation formula to find the time taken at 7.5 miles per hour.
Step-by-step explanation:
In this problem, the time it takes to travel a fixed distance is said to vary inversely with the speed traveled. This means that as the speed increases, the time taken to travel the distance decreases, and vice versa. We can use the formula for inverse variation, which is time = k/speed, where k is a constant.
Given that it takes Carson 60 minutes to bike to her fishing spot at 5 miles per hour, we can set up the equation as follows: 60 = k/5. To solve for k, we multiply both sides by 5: k = 300.
Now, we can use the value of k to find out how long it will take Carson to ride at 7.5 miles per hour. Plugging in the values into the formula, we have: time = 300/7.5. Solving for time, we get: time = 40 minutes.