A thief steals a car at 4 pm and drvies it at 80 kmph. The theft is discovered by police at 4:45 pm and sets off in another car at 100 kmph. When will the police overtake the thief ?

Options

A. 07 : 30 am
B. 07 : 45 pm
C. 07 : 30 pm
D. 06 : 45 pm

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Determine the time difference between the thief and the police.
The thief starts driving at 4:00 PM, and the police discover the theft at 4:45 PM. Therefore, the time difference is:
- **Time difference = 4:45 PM - 4:00 PM = 45 minutes.**

**Hint:** Convert the time difference into hours for easier calculations.

### Step 2: Convert the time difference into hours.
Since 45 minutes is not in hours, we convert it:
- **45 minutes = 45/60 hours = 3/4 hours.**

**Hint:** Remember that 1 hour = 60 minutes, so to convert minutes to hours, divide by 60.

### Step 3: Calculate the distance the thief has traveled by the time the police start.
The thief drives at a speed of 80 km/h. To find out how far he has traveled in 3/4 hours:
- **Distance = Speed × Time = 80 km/h × (3/4) h = 60 km.**

**Hint:** Use the formula for distance: Distance = Speed × Time.

### Step 4: Determine the relative speed between the police and the thief.
The police drive at a speed of 100 km/h, while the thief drives at 80 km/h. The relative speed when both are moving in the same direction is:
- **Relative Speed = Speed of Police - Speed of Thief = 100 km/h - 80 km/h = 20 km/h.**

**Hint:** When two objects are moving in the same direction, subtract their speeds to find the relative speed.

### Step 5: Calculate the time taken for the police to catch up with the thief.
Using the lead distance (60 km) and the relative speed (20 km/h), we can find the time it takes for the police to catch up:
- **Time = Lead Distance / Relative Speed = 60 km / 20 km/h = 3 hours.**

**Hint:** The formula for time is Time = Distance / Speed.

### Step 6: Determine the time when the police will overtake the thief.
The police start their pursuit at 4:45 PM. Adding the time taken to catch up (3 hours):
- **Time of Overtake = 4:45 PM + 3 hours = 7:45 PM.**

**Hint:** When adding hours to a specific time, ensure you keep track of AM/PM.

### Final Answer:
The police will overtake the thief at **7:45 PM**.