A, B and C are on a trip by car. A drives during the first hour at an average speed 50 `"km"//"hr"`. B drives during the next 2 hours at an average speed of 48 `"km"//"hr"`. A and C drives during the next 3 hours at an average speed of 52 `"km"//"hr"` and they reached the destination in 6 hours. Their mean speed is:

Options

A. 50 `"km"//"hr"`
B. `50 1/3 "km"//"hr"`
C. 51 `"km"//"hr" 1/3`
D. 52 `"km"//"hr"`

Answer

To find the mean speed of A, B, and C during their trip, we can follow these steps:

### Step 1: Calculate the distance covered by A during the first hour.
- A drives at an average speed of 50 km/hr for 1 hour.
- Distance = Speed × Time = 50 km/hr × 1 hr = 50 km.

### Step 2: Calculate the distance covered by B during the next two hours.
- B drives at an average speed of 48 km/hr for 2 hours.
- Distance = Speed × Time = 48 km/hr × 2 hr = 96 km.

### Step 3: Calculate the distance covered by A and C during the next three hours.
- A and C drive at an average speed of 52 km/hr for 3 hours.
- Distance = Speed × Time = 52 km/hr × 3 hr = 156 km.

### Step 4: Calculate the total distance covered.
- Total Distance = Distance by A + Distance by B + Distance by A and C
- Total Distance = 50 km + 96 km + 156 km = 302 km.

### Step 5: Calculate the mean speed.
- Mean Speed = Total Distance / Total Time
- Mean Speed = 302 km / 6 hr = 50.33 km/hr (approximately).

### Final Answer:
The mean speed of A, B, and C during their trip is approximately **50.33 km/hr**.

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