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"To stop a car, first you require a certain reaction time to begin braking; then the car slows under the constant braking deceleration. Suppose that the total distance moved by your car during these two phases is 56.7 m when its initial speed is 80.5 km/h, and 24.4 m when its initial speed is 48.3 km/h. What are (a) your reaction time and (b) the magnitude of the deceleration" (Fundamentals of Physics 6th ed; Halliday, Resnick, and Walker; pg 29, #37)

I've set the problem up, graphed the data, manipulated a lot of equations, and tried to solve it geometrically. I suspect that I need to use ratios to relate the two different situations, solve for reaction time, and use that to find acceleration, but I can't see how to do it.

Please Help!