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.
