Final answer:
By calculating the distance to his uncle's place and determining the time taken at a new speed of 65 mph, Rohan will reach approximately 55 minutes sooner than at a speed of 55 mph.
Step-by-step explanation:
Rohan can drive to his uncle's place in 6 hours at an average speed of 55 miles per hour. To calculate how much sooner he would reach if he drives at an average speed of 65 miles per hour, we first need to calculate the distance to his uncle's place using his initial average speed and time:
Distance = Speed × Time = 55 mph × 6 h = 330 miles.
Now, we use this distance to determine the time it would take Rohan when driving at 65 miles per hour:
Time at 65 mph = Distance ÷ New Speed = 330 miles ÷ 65 mph = 5.08 hours.
To find out how many hours sooner he would reach, we subtract the time taken at the new speed from the original time:
Time Saved = Original Time - New Time = 6 h - 5.08 h = 0.92 hours.
This means Rohan will reach his uncle's place 0.92 hours sooner, which is about 55 minutes faster.