Final answer:
Mike's average speed for the total trip, after calculating the distances covered during each segment and summing up the total time, is approximately 53.12 km/h.
Step-by-step explanation:
To calculate Mike's average speed for the total trip, we need to find the total distance covered and the total time taken and then use the formula average speed = total distance / total time.
First, we convert the time into hours: 10 minutes is 10/60 hours (or 1/6 hours), and 1 hour 7 minutes is 1 + 7/60 hours (or 67/60 hours).
Now we calculate the distance covered in each segment of the trip: For the first segment at 57 km/h for 1/6 hours, the distance is 57 * (1/6) = 9.5 km. For the second segment at 52 km/h for 67/60 hours, the distance is 52 * (67/60) = 58.53 km.
The total distance covered is 9.5 km + 58.53 km = 68.03 km. The total time spent is 1/6 hours + 67/60 hours = 77/60 hours.
The average speed is then total distance divided by total time, which gives us 68.03 km / (77/60) hours = 53.12 km/h.
Therefore, Mike's average speed for the total trip is approximately 53.12 km/h.