Question

Two cars simultaneously started traveling towards each other from two cities, which are 400 miles apart. Car 1 travels 20mph faster than Car 2, and they met in 4 hours. What are the speeds of the cars?

Answer 1

The first car travels at 60 mph and the second at 40 mph.

Explanation:

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Answer 2

The first car travels at 60 mph and the second at 40 mph.

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.