# Calculus Problem-Need FAST!

• Dec 15th 2007, 05:55 PM
Th3On3Fr33man
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.
• Dec 15th 2007, 06:05 PM
galactus
This shouldn't take calculus to figure out. Think about it. He travelled 5 miles in 4 minutes.
• Dec 15th 2007, 06:07 PM
Th3On3Fr33man
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
• Dec 15th 2007, 06:10 PM
Soltras
Quote:

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.

Average speed is $\frac{distance}{time} = \frac{ 5 mi. }{ 4 min. } = 75 mph$

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.
• Dec 15th 2007, 06:13 PM
Th3On3Fr33man
Thanks Soltras