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.

Question

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

Good job.

Thanks very much

Answer 1

You're welcome! I'm glad I could help explain the concept of using an indirect proof to prove that John exceeded the 55 MPH speed limit. The key is to assume the opposite of what you want to prove and then show that it leads to a contradiction. By assuming that John traveled at a constant speed of 55 mph and calculating the distance he would have covered in the given time frame, we can see that he would not have made it to his office. This contradicts the known fact that he did make it to his office, which means he must have traveled at a speed greater than 55 mph.