Calculus Problem-Need FAST!

Two stationary patrol cars equipped with radar are 5 miles apart on Highway 41. As Alex's car passes the first patrol car, its speed is clocked at 55 mph. Four minutes later, when Alex passes the second patrol car, his speed is clocked at 50 miles per hour. Prove that Alex must have exceeded the 55 mph speed limit at some time during that four minutes and deserves his speeding ticket. Use Calculus.

This shouldn't take calculus to figure out. Think about it. He travelled 5 miles in 4 minutes.

I know, it seemed the same way to me, I could've figured it out that way, the teacher wants it solved ONLY through Calculus, with all the work, thats why she put that at the end :p

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Originally Posted by Th3On3Fr33man

Two stationary patrol cars equipped with radar are 5 miles apart on Highway 41. As Alex's car passes the first patrol car, its speed is clocked at 55 mph. Four minutes later, when Alex passes the second patrol car, his speed is clocked at 50 miles per hour. Prove that Alex must have exceeded the 55 mph speed limit at some time during that four minutes and deserves his speeding ticket. Use Calculus.

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Average speed is

Now, since you have to use Calculus, quote the mean value theorem -- there must have been some point in those four miles at which Alex was going exactly 75 mph.

Thanks Soltras