Answer:
The first car travels at 60 mph and the second at 40 mph.
Step-by-step explanation:
Let's represent the speed of the first car as s1 and that of the second car as s1. Then s1 = s2 + 20 reflects the fact that the speed of the first car is 20 mph faster than that of the second car.
The total distance traveled is 400 miles. Since distance = rate times time,
time = distance / rate.
First car: (s1*t) is the distance traveled;
Second car: (s2*t) is the distance traveled.
Adding these two distances together results in 400 miles:
s1*t + s2*t = 400 miles, or
t(s1 + s2) = 400 miles. Let's eliminate s1 by substituting s2+ 20 for it:
t(s2 + 20 + s2) = 400 miles. But we know t: the cars both travel 4 hours.
Thus,
(4 hr)(2s2 + 20) = 400 miles, or
(after dividing both sides by 4 hr)
(2s2 + 20) = 100 miles/hr
Subtracting 20 from both sides:
2s2 = 80, so that s2 = 40 mph.
If s2 = 40 mph, then s1 = s2 + 20 = 60 mph
The first car travels at 60 mph and the second at 40 mph.
