Two cars leave the same location traveling in opposite directions. one car leaves at 3: 00 p. m. traveling at an average rate of 55 miles per hour. the other car leaves at 4: 00 p. m. traveling at an average rate of 75 miles per hour. let x represent the number of hours after the first car leaves. how many hours after the first car leaves will the two cars be 380 miles apart?

Let the first car travel east (to the right) and the second car west (to the left).  Call the distances traveled e and w respectively.  

The first car starts out an hour before the second car (that is, at hour 0), traveling at 55 mph.  During the first hour, this car travels 55 miles east.  A general equation for the distance traveled from the starting point as a function of x (time) is e=(55 mph)(1 hour) + (55mph)x

The other car starts out at time = 1 hour, at 75 mph.  A general equation for the distance traveled from the same starting point as a function of x is then w = (75 mph)x.

We want to know when the total distance traveled in opposite directions by the two cars is e + w = (55 miles) + (55 mph)x + (75 mph)x = 380 mi

Solve for x.  55 miles + (55+75)(mph)x = 380 miles
                                      (130 mph)x =     325 miles
                                    Divide both sides by (130 mph):

(130 mph) x              325 miles
 =   = 2.5 hours (answer)
 (130 mph)              13 mph