Question 181967
Let the distance traveled by the car leaving from Atlanta be x
Then the distance traveled by the car leaving from Valdosta is 300 - x
Since the cars left at the same time, their time to the “meeting spot” will be the same
Therefore, time taken by the car leaving from Atlanta to the “meeting spot” equals the time taken by the car leaving from Valdosta to the “meeting spot”
This means that {{{x/70=(300-x)/55}}}


Cross-multiplying, we get: 55x  =  21,000 – 70x
125x  =  21000
x   =   168

Therefore, the distance traveled by the car leaving from Atlanta to Valdosta is 168 miles.


Therefore, the time it takes each car to meet = {{{168/70}}} or {{{132/55}}} These both equal 2.4 hours, or 2 hours, 24 minutes.

This means that since they both left at 12:00noon, they will meet 2 hours, 24 minutes later, or 2:24pm.

Since south of Atlanta indicates the car that left from Atlanta (north) to Valdosta (south), then they would meet 168 miles south of Atlanta.