A motorcycle leaves colorado springs, colorado, traveling north on I25 at an average speed of 47 mph. one hour later, a car leaves colorado springs, traveling south on I-25 at an average speed of 54 mph. How long after the motorcycle leaves will it take until they are 52 miles apart?

Question

A motorcycle leaves colorado springs, colorado, traveling north on I25 at an average speed of 47 mph. one hour later, a car leaves colorado springs, traveling south on I-25 at an average speed of 54 mph. How long after the motorcycle leaves will it take until they are 52 miles apart?

Answer 1

let the time driven by 1st bike be t hrs

then the time driven by 2nd bike is t-1 hrs

distance covered by 1st bike = 47t miles
distance covered by 2nd bike = 54(t-1)

47t + 54(t-1) = 52
47t + 54t - 54 = 52
101t = 106
t = 106/101 hrs or appr 1 hr and 3 minutes

Answer 2

To solve this problem, we can use the concept of relative speed. The relative speed is the combined speed at which the motorcycle and the car are moving away from each other.

First, let's calculate the relative speed of the motorcycle and the car. Since they are traveling in opposite directions, we add their speeds together:
Relative speed = speed of motorcycle + speed of car
Relative speed = 47 mph + 54 mph
Relative speed = 101 mph

Now, let's determine the time it takes until they are 52 miles apart. We'll represent this time as 't'.

Since the motorcycle leaves one hour before the car, we need to find the time for the car to travel the same duration as the motorcycle plus an extra hour:
Time for car = t + 1

Distance traveled by the car = speed × time
Distance traveled by the car = 54 mph × (t + 1)

Distance traveled by the motorcycle = speed × time
Distance traveled by the motorcycle = 47 mph × t

As they are moving away from each other, the sum of the distances traveled by the motorcycle and the car will be equal to the distance between them:
Distance traveled by the motorcycle + Distance traveled by the car = 52 miles

Substituting the values we calculated:
47 mph × t + 54 mph × (t + 1) = 52 miles

Now, we can solve this equation to find the value of 't'.

47t + 54t + 54 = 52
101t + 54 = 52
101t = 52 - 54
101t = -2
t = -2 / 101
t ≈ -0.02 hours

The result t ≈ -0.02 hours implies that the motorcycle and the car will be 52 miles apart in negative time, which doesn't make sense in this context. It seems there might be an error in the question or the information provided. Double-checking the values and the problem statement is recommended.