Annie and Ashlyn are running on a straight track They start

Annie and Ashlyn are running on a straight track. They start at the same time and both from the same position X. Annie runs a steady 3 meters/second the whole way. Ashlyn starts and runs 4 meters/second for the 1st kilometer, then slows to 2 meters/second. At what distance from the start does Annie catch Ashlyn?

Solution

Annie DATA:
rate = 3 m/sec ; distance = x meters ; time = d/r = x/3 seconds
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Ashlyn starts and runs 4 meters/second for the 1st kilometer, then slows to 2 meters/second.
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Aslyn DATA:
1st kilometer:
rate = 4 m/sec ; distance = 1000 meters ; time = d/r = 1000/4 = 250 seconds
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Rest of the distance:
rate = 2 m/sec ; distance = x-1000 meters ; rime = (x-1000)/2 seconds
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Equation:
Annie time = Total Aslyn time
x/3 = 250 + (x-1000)/2
Multiply thru by 6 to get:
2x = 1500 + 3(x-1000)
2x = 1500 + 3x - 3000
x = 1500 meters
At what distance from the start does Annie catch Ashlyn?
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Annie catches Aslyn after x = 1500 meters.