Question

Two cars leave Denver at the same time and travel in opposite directions. One car travels 10 mi/h faster than the other car. The cars are 500 mi apart in 5 h. How fast is each car traveling?

Answer 1

Let one car travel at x mph

The other car travels at x+10 mph

Their combined speed is 2x+10 mph.

Distance = 500

time = 500 /2x+10 =5

10x+50=500

10x= 450

x=45 speed of one car

The other car travels at 45+10 = 55 mph

Answer 2

The speed of one car is 'S'. The speed of the other car is (S + 10).

In 5 hours, the first car travels (5S) miles, and the other car travels 5(S + 10) miles.

Since they're going in opposite directions, the distance between them at any time
is the sum of the distance that each one has traveled.

500 = (5S) + 5(S + 10)

500 = 5S + 5S + 50

500 = 10S + 50

Subtract 50 from each side:

450 = 10S

Divide each side by 10

S = 45

S + 10 = 55