Acar traveling at 60 mph leaves ithaca and travels west. two hours later, a truck traveling at 55 mph leaves elmira and travels east. altogether, the car and truck travel 407.5 miles. how many hours does the car travel?

Identify your variables and then list what you know about them:
car's speed:  60 mph
time initially traveled by car:  2 hours
distance the car has traveled west after 2 hours:  (60 mph)(2 hr) = 120 mi

truck's speed:  55 mph
distance traveled by truck in h hours:  (55 mph)h
distance traveled by car = initial 120 miles plus (60 mph)h

total distance traveled by both vehicles:

(55 mph)h + 120 miles + (60 mph)h = 407.5 miles

Solve this equation for the time, h, and then add 2 hours to your result:

(55 mph + 60 mph)h + 120 mi = 407.5 mi

(115 mph)h = 287.5 mi.  Solve this for h.  Remember that when h was 0, the car had already been traveling 2 hours.  Thus, add 2 hours to h to obtain your final  "how many hours does the car travel?"