Question

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?

Answer 1

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