A person covers a distance from A to B at a speed of 12 km/h and B to A at a speed of 15 kmph. The total time is taken 9 hours, find the distance from A to B.

Options

A. 60 km
B. 70 km
C. 80 km
D. 90 km

Answer

To solve the problem, we will use the formula for distance, speed, and time. The relationship is given by:

\[ \text{Distance} = \text{Speed} \times \text{Time} \]

Let the distance from A to B be \( d \) kilometers.

### Step 1: Calculate Time Taken for Each Journey
1. **Time taken from A to B** at a speed of 12 km/h:
\[ \text{Time}_{AB} = \frac{d}{12} \]

2. **Time taken from B to A** at a speed of 15 km/h:
\[ \text{Time}_{BA} = \frac{d}{15} \]

### Step 2: Set Up the Equation for Total Time
According to the problem, the total time taken for the journey from A to B and back from B to A is 9 hours. Therefore, we can write the equation:
\[ \frac{d}{12} + \frac{d}{15} = 9 \]

### Step 3: Find a Common Denominator
To solve this equation, we need to find a common denominator for the fractions. The least common multiple of 12 and 15 is 60.

Rewriting the equation:
\[ \frac{5d}{60} + \frac{4d}{60} = 9 \]

### Step 4: Combine the Fractions
Now we can combine the fractions:
\[ \frac{5d + 4d}{60} = 9 \]
\[ \frac{9d}{60} = 9 \]

### Step 5: Solve for \( d \)
To eliminate the fraction, multiply both sides by 60:
\[ 9d = 540 \]
Now, divide both sides by 9:
\[ d = 60 \]

### Conclusion
The distance from A to B is **60 kilometers**.

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