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## Homework Statement

In many countries, automatic number plate recognition is used to catch speeders. The system takes a time-stamped license plate photo at one location (like an on-ramp to a freeway), and then takes a second time-stamped photo at a second location a known distance from the first location (like an exit ramp off a freeway). Since the systems knows both the distance traveled and the time you took to travel that distance, it can determine if, on average, you were speeding, and subsequently mail the car owner a complementary ticket.

Let us say you are traveling along such a highway where the speed limit is 90 km/h (25m/s). Watching the distance markers on the side of the road, you discover at the half-way point you have been traveling at a speed of 114 km/h (31.67 m/s). What maximum constant speed must you travel for the last half of the trip to avoid your parents (who own the car) getting a speeding ticket in the mail?

## Homework Equations

v(avg) = (v(max)-v(initial))/Δt

v(avg) = v(speed limit)

## The Attempt at a Solution

I set the two equations equal to one another to find v(max) since we are given v(initial) and given the speed limit. However, I don't know how to find Δt. I have tried several different ways on paper and come to no conclusion. Help please.