Distance Problem..help pls...thanks!?

Question

Two runners starting at the same time, run towards each other from the opposite ends of an 8-mile trail. One runner is running at a rate of 5 mph, and the other is running at a rate of 7 mph. How long after they start will the two runners meet?

Answer 1

What do we know? The total distance run by both runners will be 8 miles AND the time run by both will be the same when they meet.

.distance runner 1 = rate #1 x time #1

.+distance runner 2 = rate #2 x time #2

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.= 8 miles               =    5 x t  +  7 x t  =  12t

8 = 12t

8/12 = t = 2/3 hour = 40 min.

Answer 2

They are approaching each other @ 12mph so to cover 8m the need 8/12 hours or 2/3 hr or 40min.

Answer 3

Distance equals rate times time.  The distance run by the first runner at time t is 5t.  The distance run by the second runner at time t is 7t.  The two runners will meet when the sum of their distances equals 8 (because it's an 8-mile trail).

5t+7t=8

12t=8

t=8/12 or 2/3 hour or 40 minutes.

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