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Two runners run the same course. The first runner takes twice as long to run the course as the second runner. If the first runner runs at 6 mph and the second runner runs at 9 mph, how long does it take each of them to run the race?

*Set up the equation for me.

Answer :

The first runner takes 18/3 = 6 hours to run the race.

The second runner takes 18/9 = 2 hours to run the race.

Let the distance of the course be x miles.

We know that the first runner takes twice as long to run the course as the second runner, so the first runner's time is 2x/6 = x/3 hours.

We also know that the second runner runs at 9 mph, so the second runner's time is x/9 hours.

We can now set up a system of equations to solve for x:

x/3 = x/9 + t

x = 3t

t = x/3

Now that we know the time each runner takes to run the race, we can substitute it into the following equations to find the distance of the course:

x/3 = 6

x = 18 miles

Therefore, the distance of the course is 18 miles.

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