Use an indeirect 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.

Assume temporarily that John traveled at a constant speed of 55 mph and that was his maximum speed. Then in 45 minutes (8:15 am to 9:00 am), he would have traveled
55 * 3/4 = 41.25 miles and would not have made it to his office. But this contradicts the known fact that he must have traveled more than 55mph. Since he did make it to his office which is 60 miles away, he must have traveled more than 55 mph

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