A car travels a distance of 45 km at a speed of 15 km/hr. It covers the next 50 km of its journey at the speed of 25 km/hr and the last 25 km of its journey at the speed of 15 km/hr. What is the average speed of the car?

Options

A. 40 km/hr
B. 24 km/hr
C. 15 km/hr
D. 18 km/hr

Answer

To find the average speed of the car, we will follow these steps:

### Step 1: Calculate the time taken for each segment of the journey.

1. **First Segment:**
- Distance = 45 km
- Speed = 15 km/hr
- Time = Distance / Speed = 45 km / 15 km/hr = 3 hours

2. **Second Segment:**
- Distance = 50 km
- Speed = 25 km/hr
- Time = Distance / Speed = 50 km / 25 km/hr = 2 hours

3. **Third Segment:**
- Distance = 25 km
- Speed = 15 km/hr
- Time = Distance / Speed = 25 km / 15 km/hr = 5/3 hours (or approximately 1.67 hours)

### Step 2: Calculate the total time taken for the entire journey.

- Total Time = Time for First Segment + Time for Second Segment + Time for Third Segment
- Total Time = 3 hours + 2 hours + (5/3 hours)
- To add these, convert 3 hours and 2 hours into fractions:
- 3 hours = 9/3 hours
- 2 hours = 6/3 hours
- Total Time = (9/3 + 6/3 + 5/3) = (20/3) hours

### Step 3: Calculate the total distance traveled.

- Total Distance = Distance of First Segment + Distance of Second Segment + Distance of Third Segment
- Total Distance = 45 km + 50 km + 25 km = 120 km

### Step 4: Calculate the average speed.

- Average Speed = Total Distance / Total Time
- Average Speed = 120 km / (20/3) hours
- To divide by a fraction, multiply by its reciprocal:
- Average Speed = 120 km * (3/20) = 18 km/hr

### Final Answer:
The average speed of the car is **18 km/hr**.

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