A man drove to work at an average rate of speed of 60 miles per hour and returned over the same route driving at an average rate of speed of 40 miles per hour. If his total driving time was 1 hour, what was the total number of miles in the round trip?

Options

A. `12`
B. `24`
C. `30`
D. `48`

Answer

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

1. **Define Variables**:
Let the distance from the man's home to work be \( x \) miles. Therefore, the total round trip distance will be \( 2x \) miles.

2. **Calculate Time for Each Leg of the Trip**:
- For the trip to work at 60 miles per hour, the time taken \( t_1 \) can be calculated using the formula:
\[ t_1 = \frac{x}{60} \]
- For the return trip at 40 miles per hour, the time taken \( t_2 \) is:
\[ t_2 = \frac{x}{40} \]

3. **Set Up the Total Time Equation**:
According to the problem, the total driving time for both trips is 1 hour. Therefore, we can write:
\[ t_1 + t_2 = 1 \]
Substituting the expressions for \( t_1 \) and \( t_2 \) gives us:
\[ \frac{x}{60} + \frac{x}{40} = 1 \]

4. **Find a Common Denominator**:
The least common multiple of 60 and 40 is 120. We can rewrite the equation:
\[ \frac{2x}{120} + \frac{3x}{120} = 1 \]
This simplifies to:
\[ \frac{5x}{120} = 1 \]

5. **Solve for \( x \)**:
Multiply both sides by 120 to eliminate the fraction:
\[ 5x = 120 \]
Now, divide both sides by 5:
\[ x = 24 \]

6. **Calculate the Total Round Trip Distance**:
Since the round trip distance is \( 2x \):
\[ 2x = 2 \times 24 = 48 \]

Thus, the total number of miles in the round trip is **48 miles**.