A man is driving to his workplace at five-eighths of his usual speed. He reaches his workplace 36 minutes late. What is his usual time (in hours) of travel?

Options

A. 1
B. `2.5`
C. 2
D. `1.5`

Answer

To solve the problem, we need to determine the man's usual time of travel to his workplace based on the information given about his speed and the delay he experienced.

### Step-by-Step Solution:

1. **Understand the relationship between speed, time, and distance**:
The formula connecting speed (S), time (T), and distance (D) is:
\[ D = S \times T \]
If the speed decreases, the time taken to cover the same distance increases.

2. **Let the usual speed be \( S \) and the usual time be \( T \)**:
Since he is driving at five-eighths of his usual speed, his new speed is:
\[ \text{New Speed} = \frac{5}{8} S \]

3. **Calculate the time taken at the new speed**:
The time taken to cover the same distance at the new speed can be expressed as:
\[ \text{New Time} = \frac{D}{\text{New Speed}} = \frac{D}{\frac{5}{8} S} = \frac{8D}{5S} \]
Since \( D = S \times T \), we can substitute for \( D \):
\[ \text{New Time} = \frac{8(S \times T)}{5S} = \frac{8T}{5} \]

4. **Set up the equation based on the delay**:
According to the problem, the man is 36 minutes late. Therefore, the difference in time between the new time and the usual time is:
\[ \text{New Time} - \text{Usual Time} = 36 \text{ minutes} \]
Converting 36 minutes to hours gives us:
\[ 36 \text{ minutes} = \frac{36}{60} \text{ hours} = 0.6 \text{ hours} \]
Thus, we have:
\[ \frac{8T}{5} - T = 0.6 \]

5. **Solve the equation**:
Rearranging the equation gives:
\[ \frac{8T}{5} - \frac{5T}{5} = 0.6 \]
\[ \frac{3T}{5} = 0.6 \]
Multiplying both sides by 5:
\[ 3T = 3 \]
Dividing both sides by 3:
\[ T = 1 \text{ hour} \]

### Final Answer:
The man's usual time of travel is **1 hour**.