It took Sara a total of 42 minutes to jog from home to the park and back again, by the same path. If she averaged 8 miles per hour going to the park and 6 miles per hour coming back, what is the distance from her home to the park?

Explanation

To solve this problem, apply the formula Time = Distance/Speed. Let the distance one way be d miles. For the trip to the park, the time taken is d/8 hours, and for the return trip, it is d/6 hours. The total time for both trips is given as 42 minutes, equivalent to 0.7 hours. Thus, the equation is d/8 + d/6 = 0.7. Solving this equation by finding a common denominator (24), we get: 3d + 4d = 16.8, which simplifies to 7d = 16.8. Solving for d results in d = 2.4 miles. Therefore, Option A is correct. The other options (2.8, 3.2, 3.6 miles) overestimate the distance, leading to a time greater than 0.7 hours, and are incorrect.