Two cars leave town going in opposite directions. one car is traveling 55 miles per hour (mph), and the other car is traveling 40 mph. how long will it take before the cars are 285 miles apart?

The distance, d, traveled by a car going at speed, s, in time, t, is

d = st

Car 1 travels distance 1, d1, at s1 = 55 mph, for t1 time.

Car 2 travels distance 2, d2, at s2 = 40 mph, for t2 time.

The two distances add to 285 miles, so

d1 + d2 = 285

The two times are equal, so t1 = t2 = t

d1 = 55t1

d2 = 40t2

d1 = 55t

d2 = 40t

d1 + d2 = 55t + 40t

d = 95t

285 = 95t

95t = 285

t = 3

Answer: It will take 3 hours.

Note:

This problem shows you that if two cars are traveling along the same line in opposite directions, the speed at which they are distancing themselves is the sum of the two speeds. We can solve the problem in a simpler way:

55 mph + 40 mph = 95 mph

d = st

285 = 95t

t = 3

Answer: 3 hours.