Car A leaves a city at-5 pm and is driven at a speed of 30 km/hr. 3 hours later, another car B leaves the city in the same direction as car A. In how much time will car B be 12 km ahead of car A if the speed of car B is 50. km/hr?

Options

A. 5 hrs
B. 4 hrs 12 mins
C. 8 hrs
D. 5 hrs 6 mins

Answer

To solve the problem, we need to determine how long it will take for Car B to be 12 km ahead of Car A after Car B starts its journey.

### Step-by-Step Solution:

1. **Determine the time Car A travels before Car B starts:**
- Car A leaves at 5 PM and travels for 3 hours before Car B starts.
- Therefore, Car A starts at 5 PM and travels until 8 PM.

2. **Calculate the distance traveled by Car A in those 3 hours:**
- Speed of Car A = 30 km/hr
- Distance = Speed × Time
- Distance traveled by Car A in 3 hours = 30 km/hr × 3 hr = 90 km

3. **Determine the relative speed of Car B with respect to Car A:**
- Speed of Car B = 50 km/hr
- Speed of Car A = 30 km/hr
- Relative speed of Car B = Speed of Car B - Speed of Car A = 50 km/hr - 30 km/hr = 20 km/hr

4. **Set up the equation to find the time it takes for Car B to be 12 km ahead of Car A:**
- Car B needs to cover the initial distance of 90 km (the distance Car A has already traveled) plus the additional 12 km to be ahead.
- Total distance Car B needs to cover = 90 km + 12 km = 102 km

5. **Calculate the time taken by Car B to cover this distance at the relative speed:**
- Time = Distance / Speed
- Time taken by Car B = 102 km / 20 km/hr = 5.1 hours

### Final Answer:
Car B will be 12 km ahead of Car A in 5.1 hours after it starts its journey.