Question 404271
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 {{{1/6}}}x and the second athletes distance is given by {{{1/8}}}x + 2.
:
(a) When are the athletes the same distance from the parking lot?
{{{1/6}}}x = {{{1/8}}}x + 2
{{{1/6}}}x - {{{1/8}}}x = 2
Common denominator is 24
{{{4/24}}}x - {{{3/24}}}x = 2
{{{1/24}}}x = 2
Multiply both sides by 24
1x = 24(2)
x = 48 minutes
:
We can check this: 
{{{1/6}}}(48) = {{{1/8}}}(48) + 2
:
:
(b) When is the first athlete farther away from the parking lot than the second?
{{{1/24}}}x > 2
x > 48 minutes, Say 49 minutes
{{{1/6}}}(49) = 8.167 mi
{{{1/8}}}(49) + 2 = 8.125 mi