SOLUTION: Nick and Scott leave opposite ends of a bike trail 13 mi apart and travel toward each other. Scott is traveling 2 mph slower than Nick. Find each of their speeds if they meet after

Question 504626: Nick and Scott leave opposite ends of a bike trail 13 mi apart and travel toward each other. Scott is traveling 2 mph slower than Nick. Find each of their speeds if they meet after 30 minutes.
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
Nick and Scott leave opposite ends of a bike trail 13 mi apart and travel toward each other. Scott is traveling 2 mph slower than Nick. Find each of their speeds if they meet after 30 minutes.
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To solve, we could consider their individual distances and speeds, but we can also solve using their RELATIVE speed.
If s = Nick's speed, then Scott's speed = s - 2
The relative speed s + s - 2 = 2s - 2
So the two riders approaching one another is the same as one rider standing
still and the other approaching at speed 2s - 2
The 13 mile distance is covered in 30 min.
So we can solve for s using
2s - 2 = 13 mi/0.5 h
2s = 28
s = 14 mi/h
So Scott's speed = 12 mi/h
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