Bad boy is fleeing the scene of a crime at 75 mph. Half an hr. later the police chase after him following his same route-traveling at 90 mph. Bad boy thought he got away... but he didn't...
How long had Bad boy been traveling when the police caught him?
To find out how long the bad boy had been traveling when the police caught him, we need to determine the time it took for the police to catch up with him.
Let's break down the information given:
- The bad boy is traveling at a speed of 75 mph.
- The police start chasing him half an hour later.
- The police are traveling at a speed of 90 mph.
Since the police start chasing the bad boy half an hour later, this means the bad boy has a head start of half an hour.
To find out the distance the bad boy travels during this half-hour head start, we can use the formula: distance = speed * time.
Distance traveled by the bad boy = 75 mph * 0.5 hr = 37.5 miles.
Now, both the bad boy and the police are traveling on the same route. The police are traveling at a speed of 90 mph. So, the relative speed of the police to the bad boy is (90 mph - 75 mph) = 15 mph.
To catch up with the bad boy, the police need to cover the same distance the bad boy traveled during his half-hour head start, which is 37.5 miles.
Using the formula again, we can find the time it takes for the police to cover this distance: time = distance / speed.
Time taken by the police = 37.5 miles / 15 mph = 2.5 hours.
Therefore, the bad boy had been traveling for 0.5 hours (30 minutes) plus 2.5 hours, which equals 3 hours when the police caught him.