Need an Indirect Proof for this (has to do with speed limits and miles driven).?

Question

I am good at doing indirect proofs,with geometric figures,but this kind of problems always confuse me. So plzz help me out.


Use an indirect proof to show that John exceeded the 55 mph speed limit if he left his house at 8:15 a.m. and arrived at his office 60 miles away at 9:00 a.m. Write the proof using paragraph method.

ok, the first step is to "assume temporarily that the conclusion is false, and then ...". IS INDIRECT PROOF.

Answer 1

Time taken = 45 min = 3 / 4 hour
Average Speed = 60 / (3/4) mph
Average Speed = 60 x 4 / 3 mph
Average Speed = 80 mph
John exceeded the 55 mph speed limit.

Answer 2

Let x = John's speed in mph.

Equation:
(9:00 - 8:15) * x = 60
3/4x = 60
x = 80

Answer: John's speed was 80 mph and therefore he exceeded the 55 mph speed limit.

Another way of knowing if he exceeded 55 mph speed limit.

Let x = time period in hours to reach 60 miles at 55 mph.

Equation:
55x = 60
x = 60/55 or 12/11 or 1 1/11 hours.

Answer: If his speed limit is 55 mph he could have traveled the 60 mile distance for 1 1/11 hours. But as it is, he reached his office in only 45 minutes (8:15—9 AM) and so he traveled exceeding the 55 mph speed limit.

Answer 3

The average speed is the lowest possible maximum speed during the drive. If he had varied speed at all, there would be a higher maximum, so assuming that under the best possible conditions, he never had to accelerate and was always going at the average speed...
60 miles / .75 hours = average of 80 mph so he was going at the very least 80 miles per hour for the maximum speed.

Answer 4

If John traveled 60 miles in .75 hours then his average speed was 80 miles per hour.
I don't know how to state this 'indirectly' as the mathematics is spelled out so obviously, simply, and explicitly.