A motorcycle leaves Colorado Springs traveling north at an average speed of 47 miles per hour. One hour later, a car leaves Colorado Springs traveling south at an average speed of 54 miles per hour. How long after the motor cycle leaves will it take until they are 552 miles apart?
To solve this problem, we can set up a distance equation.
Let's consider the time elapsed after the motorcycle leaves as "t" hours.
When the motorcycle leaves, the car has already been traveling for one hour. So, the car has been traveling for "t - 1" hours.
Since distance is equal to speed multiplied by time (d = s * t), the distance traveled by the motorcycle is 47t miles, and the distance traveled by the car is 54(t - 1) miles.
According to the problem statement, the sum of the distances traveled by the motorcycle and the car should be equal to 552 miles. Therefore, we can write the equation:
47t + 54(t - 1) = 552
Now, let's solve this equation for t:
47t + 54t - 54 = 552
101t - 54 = 552
101t = 606
t = 606 / 101
t ≈ 6
Therefore, it will take approximately 6 hours after the motorcycle leaves until they are 552 miles apart.