SOLUTION: Jack and Conner are running a race. Jack has an average speed of 4 mph and Conner has an average speed of 5 mph. If Jack gets a head start of 10 miles, after how long will Colin ca

Question 1092838: Jack and Conner are running a race. Jack has an average speed of 4 mph and Conner has an average speed of 5 mph. If Jack gets a head start of 10 miles, after how long will Colin catch up to him? I know how the answer is 10 hours and I found it from making a chart and finding it out from there. But how can I do it in equation form?
Answer by greenestamps(13214) (Show Source): You can put this solution on YOUR website!

You are asked for the number of hours it takes for Conner to catch up to Jack, so make that your variable:

let x = number of hours it takes for Conner to catch up to Jack

If we use Conner's starting point as the beginning, then Jack's distance from the starting point after x hours is 10+4x, because he starts 10 miles ahead of Conner and runs 4 miles each of the x hours. Conner's distance from the starting point is 5x, because he runs 5 miles each of the x hours.

You want to know when Conner catches up to Jack; that is when the distances of both of them from the starting point are the same.

So set the expressions for their distances from the starting point equal to each other and solve the resulting equation.
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