A scooter travels some distance at a speed of 12 km/hr and returns at a speed of 7 km/hr. If the total time taken by the scooter is 19 hours, then what is the distance (in km)?

Options

A. 84
B. 80
C. 72
D. 76

Answer

To solve the problem step by step, we can follow these steps:

### Step 1: Define the Variables
Let the distance traveled one way be \( D \) kilometers.

### Step 2: Calculate Time for Each Leg of the Journey
- Time taken to travel to the destination at 12 km/hr:
\[ \text{Time}_{\text{to}} = \frac{D}{12} \]
- Time taken to return at 7 km/hr:
\[ \text{Time}_{\text{return}} = \frac{D}{7} \]

### Step 3: Set Up the Equation for Total Time
According to the problem, the total time for the round trip is 19 hours. Therefore, we can write the equation:
\[ \frac{D}{12} + \frac{D}{7} = 19 \]

### Step 4: Find a Common Denominator
The least common multiple (LCM) of 12 and 7 is 84. We will multiply each term by 84 to eliminate the denominators:
\[ 84 \left(\frac{D}{12}\right) + 84 \left(\frac{D}{7}\right) = 84 \cdot 19 \]
This simplifies to:
\[ 7D + 12D = 1596 \]

### Step 5: Combine Like Terms
Combine the terms on the left side:
\[ 19D = 1596 \]

### Step 6: Solve for \( D \)
Now, divide both sides by 19 to find \( D \):
\[ D = \frac{1596}{19} = 84 \]

### Conclusion
The distance \( D \) is 84 kilometers.