Two cars leave town at the same time and travel in opposite directions. The average rate of speed of one car is 15 miles per hour faster than the average rate of speed of the other car. The cars are 315 miles apart after three hours. Find the average rate of speed of the two cars.
let r equal the speed of the slower car ... 2 r + 15 = 315 / 3
To find the average rate of speed of the two cars, we need to set up an equation based on the given information.
Let's call the average rate of speed of one car "x" miles per hour. Since the other car is traveling 15 miles per hour faster, its average rate of speed would be "x + 15" miles per hour.
When two cars are moving in opposite directions, the distance between them increases at a rate equal to the sum of their speeds. So, in three hours, the distance between the two cars is the sum of the distances each car has traveled.
The distance traveled by the first car is 3 * x miles, and the distance traveled by the second car is 3 * (x + 15) miles. Therefore, the sum of these distances should equal 315 miles, as given.
Setting up the equation:
3x + 3(x + 15) = 315
Simplifying the equation:
3x + 3x + 45 = 315
Combining like terms:
6x + 45 = 315
Subtracting 45 from both sides:
6x = 270
Dividing both sides by 6:
x = 45
So, the average rate of speed of the first car is 45 miles per hour.
The average rate of speed of the second car, which is 15 miles per hour faster, would be:
45 + 15 = 60 miles per hour.
Therefore, the average rate of speed of the two cars is 45 miles per hour and 60 miles per hour.