A man travels from Point A to B with 70 km/hr and from B to
C with 50km/hr. Total distance between A to C 300 km. If
his average speed is 60 km/hr then find the distance
between A and B?

Options

A. 80 km
B. 125 km
C. 100 km
D. 150 km

Explanation

To solve the problem step by step, we will use the information given about the speeds and the total distance to find the distance between points A and B.

### Step 1: Define the Variables
Let:
- \( x \) = distance from A to B (in km)
- \( y \) = distance from B to C (in km)

From the problem, we know that:
\[ x + y = 300 \] (Total distance from A to C)

### Step 2: Calculate Time Taken for Each Segment
The time taken to travel from A to B at a speed of 70 km/hr is:
\[ \text{Time from A to B} = \frac{x}{70} \]

The time taken to travel from B to C at a speed of 50 km/hr is:
\[ \text{Time from B to C} = \frac{y}{50} \]

### Step 3: Calculate Total Time and Average Speed
The average speed for the entire journey from A to C is given as 60 km/hr. The total distance is 300 km, so the total time taken for the journey can be calculated as:
\[ \text{Total Time} = \frac{\text{Total Distance}}{\text{Average Speed}} = \frac{300}{60} = 5 \text{ hours} \]

### Step 4: Set Up the Equation for Total Time
The total time for the journey can also be expressed as the sum of the times for each segment:
\[ \frac{x}{70} + \frac{y}{50} = 5 \]

### Step 5: Substitute \( y \) in Terms of \( x \)
From the first equation \( x + y = 300 \), we can express \( y \) as:
\[ y = 300 - x \]

### Step 6: Substitute \( y \) in the Time Equation
Now substitute \( y \) in the time equation:
\[ \frac{x}{70} + \frac{300 - x}{50} = 5 \]

### Step 7: Solve the Equation
To eliminate the fractions, we can multiply through by the least common multiple of 70 and 50, which is 350:
\[ 350 \left(\frac{x}{70}\right) + 350 \left(\frac{300 - x}{50}\right) = 350 \cdot 5 \]

This simplifies to:
\[ 5x + 7(300 - x) = 1750 \]

Expanding the equation:
\[ 5x + 2100 - 7x = 1750 \]

Combine like terms:
\[ -2x + 2100 = 1750 \]

### Step 8: Isolate \( x \)
Now, isolate \( x \):
\[ -2x = 1750 - 2100 \]
\[ -2x = -350 \]
\[ x = 175 \]

### Step 9: Find \( y \)
Now substitute \( x \) back to find \( y \):
\[ y = 300 - x = 300 - 175 = 125 \]

### Conclusion
The distance between A and B is:
\[ \boxed{175 \text{ km}} \]