SOLUTION: Distance and time: Two athletes are jogging in the same direction along an exercise path. After x minutes the first athletes distance in miles from a parking lot is given by 1/6x a

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Question 404271: Distance and time: Two athletes are jogging in the same direction along an exercise path. After x minutes the first athletes distance in miles from a parking lot is given by 1/6x and the second athletes distance is given by 1/8x + 2.
(a) When are the athletes the same distance from the parking lot?
(b) When is the first athlete farther away from the parking lot than the second?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Two athletes are jogging in the same direction along an exercise path.
After x minutes the first athletes distance in miles from a parking lot is
given by 1%2F6x and the second athletes distance is given by 1%2F8x + 2.
:
(a) When are the athletes the same distance from the parking lot?
1%2F6x = 1%2F8x + 2
1%2F6x - 1%2F8x = 2
Common denominator is 24
4%2F24x - 3%2F24x = 2
1%2F24x = 2
Multiply both sides by 24
1x = 24(2)
x = 48 minutes
:
We can check this:
1%2F6(48) = 1%2F8(48) + 2
:
:
(b) When is the first athlete farther away from the parking lot than the second?
1%2F24x > 2
x > 48 minutes, Say 49 minutes
1%2F6(49) = 8.167 mi
1%2F8(49) + 2 = 8.125 mi