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Uniform Motion Problem

A long-distance runner started on a course at an average speed of 8 mph. Half an hour later, a second runner began the same course at an average speed of 10 mph. How long after the second runner starts will the second runner overtake the first runner?

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Using the Distance Formula, D = RT where D is the distance, R is the rate of motion, and T is the time. Hence, Distance for runner 1 is D1 and distance for runner 2 is D2. Since the two runners are said to travel at the "same course", distance is equal; D1 = D2. So these are the derived equations: D1 = RT D1 = 8 (x + 1/2) D2 = RT D2 = 10 (x) ; since runner 2 travelled the least amount of time (since he started late) we call his T as x. Since D1 = D2 it gives; 8 (x + 1/2) = 10x Solving for X: 8x + 4 = 10x 4 = 10x - 8x 4 = 2x 2 = x Therefore, after 2 hours that the second runner starts, the second runner overtakes the first runner. CHECK: Distance of first runner: D1 = 8(x + 1/2) D1 = 8x + 4 D1 = 8(2)+4 D1 = 20 miles D2 = 10x D2 = 10(2) D2 = 20 miles This means that after 2 hours that the second runner starts, he will be on equal distance (20 miles) with the first runner. Since the second runner is running at a faster rate, he will start to overtake the first runner.

Using the Distance Formula, D

Using the Distance Formula, D = RT where D is the distance, R is the rate of motion, and T is the time. Hence, Distance for runner 1 is D1 and distance for runner 2 is D2. Since the two runners are said to travel at the "same course", distance is equal; D1 = D2. So these are the derived equations: D1 = RT D1 = 8 (x + 1/2) D2 = RT D2 = 10 (x) ; since runner 2 travelled the least amount of time (since he started late) we call his T as x. Since D1 = D2 it gives; 8 (x + 1/2) = 10x Solving for X: 8x + 4 = 10x 4 = 10x - 8x 4 = 2x 2 = x Therefore, after 2 hours that the second runner starts, the second runner overtakes the first runner. CHECK: Distance of first runner: D1 = 8(x + 1/2) D1 = 8x + 4 D1 = 8(2)+4 D1 = 20 miles D2 = 10x D2 = 10(2) D2 = 20 miles This means that after 2 hours that the second runner starts, he will be on equal distance (20 miles) with the first runner. Since the second runner is running at a faster rate, he will start to overtake the first runner.