A police officer is chasing a purse snatcher down a street. The thief starts 9 yards ahead of the officer and can run 20 yards in 4 seconds (5 y/s). The police officer can run 32 yards in 4 seconds (8 y/s). How long will it take the officer to catch the thief?
To find out how long it will take the police officer to catch the thief, we need to determine how much distance the officer needs to cover to reach the thief.
The thief starts 9 yards ahead of the officer, so the distance the officer needs to cover is 9 yards.
The police officer can run 8 yards per second, so we can calculate the time it will take for the officer to catch the thief by dividing the distance by the officer's speed:
Time = Distance / Speed = 9 yards / 8 y/s = 1.125 seconds
Therefore, it will take the police officer 1.125 seconds to catch the thief.
To solve this problem, we need to find out how long it will take for the police officer to cover the initial distance between them, which is 9 yards.
The thief can run 20 yards in 4 seconds, which means the thief's speed is 20 yards / 4 seconds = 5 yards per second (y/s).
The police officer can run 32 yards in 4 seconds, which means the officer's speed is 32 yards / 4 seconds = 8 yards per second (y/s).
We need to find out how long it will take for the officer to catch up to the thief, so we divide the initial distance between them (9 yards) by the difference in their speeds (8 y/s - 5 y/s = 3 y/s):
Time = Distance / Speed
Time = 9 yards / 3 y/s
Time = 3 seconds
Therefore, it will take the police officer 3 seconds to catch the thief.
To solve this problem, we need to find the time it takes for the police officer to cover the distance between him and the thief.
First, let's determine the relative distance between the two. The thief starts 9 yards ahead, so the distance the police officer needs to cover is 9 yards less than the distance the thief can run in the same amount of time.
Let's assume t represents the time in seconds it takes for the officer to catch the thief.
The distance the thief can run in t seconds is given by 5 * t.
The distance covered by the police officer in t seconds is given by 8 * t.
Since the distance the officer needs to cover is 9 yards less than the distance the thief can run, we can set up the equation:
5 * t - 9 = 8 * t
Now, let's solve for t:
5t - 9 = 8t
Subtract 5t from both sides:
-9 = 3t
Divide both sides by 3:
t = -9/3
t = -3
The solution for t is -3, which doesn't make sense in this context because we can't have a negative time. Therefore, the thief cannot be caught by the officer.
So, in this scenario, the officer will not be able to catch the purse snatcher.