hey.....
A state patrol officer saw a car start from rest at a highway on-ramp. She radioed ahead to another officer 30 mi along the highway. When the car reached the location of the second officer 26 min later, it was clocked going 60 mi/hr. The driver of the car was given a ticket for exceeding the 60/mi/hr speed limit. Why can the officer conclude that the drive exceeded the speed limit?

Question

hey.....
A state patrol officer saw a car start from rest at a highway on-ramp. She radioed ahead to another officer 30 mi along the highway. When the car reached the location of the second officer 26 min later, it was clocked going 60 mi/hr. The driver of the car was given a ticket for exceeding the 60/mi/hr speed limit. Why can the officer conclude that the drive exceeded the speed limit?

tkhunny · Answer

HINT: 60 mph = 1 mile/minute

anonymous · Answer

Can you please explain it? I really dont get it

lukebluefive · Answer

If the car was going 60mph, or 1 mile a minute, how long would it have taken the car to travel 30 miles?

anonymous · Answer

30min

tkhunny · Answer

...and...

anonymous · Answer

so 30 miles in 30 min?

lukebluefive · Answer

Right, so how is the only way the car could've travelled 30 miles in less than 30 minutes?

anonymous · Answer

if it went over 30mph?

lukebluefive · Answer

Well, a mile a minute is 60 mph, so 30 miles would take 30 minutes to travel, going that speed.  So the car wasn't just going over 30 mph, it was going over...?

anonymous · Answer

60mph

lukebluefive · Answer

Exactly, which is what you wanted to show.

anonymous · Answer

But it is telling me to use eithe Rolle's theorem, mean value theorem or extreme value theorem which one do I know to use?

anonymous · Answer

and it wants to know at some time c, the car was traveling at ___mph

lukebluefive · Answer

I think you'd use Rolle's Theorem to find that out.

anonymous · Answer

can you help me walk me through it?

lukebluefive · Answer

Actually, it's the Mean Value Theorem... Rolle's Theorem is just a specific type of it, but w/e.  Let me see if I can get brushed up enough to help you.

anonymous · Answer

thank you

tkhunny · Answer

Simplified - The average speed must have been accomplished at some time during the measurement.

Other Words - If it's continuous, it can't be the average if you don't manage it at least once.

lukebluefive · Answer

Well, first, I'd find the average speed using the following equation:
$$speed = \frac{distance} {time}$$

anonymous · Answer

ok

lukebluefive · Answer

Since the car travelled 30 miles in 26 minutes, this would be:
$$speed = \frac{30 miles}{26 minutes} = \frac{15miles}{13minutes} \times \frac{60minutes}{1hour} = \frac{900miles}{13hours} \approx 69 mph$$

anonymous · Answer

thank youuu

lukebluefive · Answer

You're welcome.  Let me know if you need help in the future.