Question

Two cars leave towns 320 kilometers apart at the same time and travel toward eachother. One car's rate is 12 kilometers per hour less than the other's. If they meet in 2 hours, what is the rate of the slower car?

Do not do any rounding.

Answer 1

74 kilometers per hour.

Explanation:

Let's call the speed of the faster car "x" (in kilometers per hour). Then, according to the problem, the speed of the slower car is "x - 12" (in kilometers per hour).

The two cars are traveling towards each other, so the distance between them decreases at a rate equal to the sum of their speeds. In other words, the relative speed between the two cars is:

x + (x - 12) = 2x - 12

According to the problem, they meet after 2 hours of travel, so the total distance they cover is:

distance = speed × time

For the faster car, the distance it covers is:

distance = x × 2

For the slower car, the distance it covers is:

distance = (x - 12) × 2

Since they are both traveling towards each other, the sum of the distances covered by both cars should be equal to the total distance between them at the start of the trip (320 kilometers):

x × 2 + (x - 12) × 2 = 320

Simplifying this equation:

2x + 2x - 24 = 320

4x = 344

x = 86

Therefore, the speed of the faster car is 86 kilometers per hour.

To find the speed of the slower car, we can use the expression we found earlier:

x - 12 = 86 - 12 = 74

Therefore, the speed of the slower car is 74 kilometers per hour.