Final answer:
Dylan spent 5 hours traveling to the study group at 4 mph and 2 hours returning home at 10 mph. This utilizes the distance-rate-time relationship to solve the problem, given the total trip time was 7 hours.
Step-by-step explanation:
The student's question involves calculating the time Dylan spent traveling at two different speeds during his round trip. Since the trip took 7 hours in total, we can use the concept of distance, rate, and time to solve the problem. Let's let t be the time Dylan traveled going to the study group, and 7 - t will be the time he spent returning home.
Distance is equal to rate multiplied by time (d = rt), so we have: For the trip to the study group: 4 mph * t = d For the return trip: 10 mph * (7 - t) = d. Since Dylan traveled the same distance to the study group as he did returning home, we can equate the two distances: 4t = 10(7 - t).Solving for t, we get: 4t = 70 - 10t 4t + 10t = 70 14t = 70 t = 70 / 14 t = 5.Hence, Dylan traveled for 5 hours at 4 mph to the study group and for 2 hours at 10 mph on the return trip home.