A person covers 20 km in a certain time. He travels four successive distances of 5 km each at respective speeds of 10 kmph, 20 kmph , 30 kmph, and 60 kmph. Find the time taken to cover the total distance

Options

A. 2 h
B. 1 h 30 min
C. 1 h
D. 30 min

Answer

To find the total time taken by the person to cover the distance of 20 km, we will calculate the time taken for each of the four successive distances of 5 km at their respective speeds.

### Step-by-Step Solution:

1. **Identify the distances and speeds**:
- The person covers 4 distances of 5 km each.
- The speeds for each distance are:
- First 5 km at 10 km/h
- Second 5 km at 20 km/h
- Third 5 km at 30 km/h
- Fourth 5 km at 60 km/h

2. **Calculate the time taken for each distance**:
- Time = Distance / Speed

- **First 5 km at 10 km/h**:
\[ \text{Time}_1 = \frac{5 \text{ km}}{10 \text{ km/h}} = 0.5 \text{ hours} \]

- **Second 5 km at 20 km/h**:
\[ \text{Time}_2 = \frac{5 \text{ km}}{20 \text{ km/h}} = 0.25 \text{ hours} \]

- **Third 5 km at 30 km/h**:
\[ \text{Time}_3 = \frac{5 \text{ km}}{30 \text{ km/h}} = \frac{1}{6} \text{ hours} \approx 0.1667 \text{ hours} \]

- **Fourth 5 km at 60 km/h**:
\[ \text{Time}_4 = \frac{5 \text{ km}}{60 \text{ km/h}} = \frac{1}{12} \text{ hours} \approx 0.0833 \text{ hours} \]

3. **Add the times together**:
\[ \text{Total Time} = \text{Time}_1 + \text{Time}_2 + \text{Time}_3 + \text{Time}_4 \]
\[ = 0.5 + 0.25 + \frac{1}{6} + \frac{1}{12} \]

4. **Finding a common denominator**:
- The least common multiple (LCM) of 1, 6, and 12 is 12.
- Convert each term to have a denominator of 12:
- \(0.5 = \frac{6}{12}\)
- \(0.25 = \frac{3}{12}\)
- \(\frac{1}{6} = \frac{2}{12}\)
- \(\frac{1}{12} = \frac{1}{12}\)

5. **Add the fractions**:
\[ \text{Total Time} = \frac{6}{12} + \frac{3}{12} + \frac{2}{12} + \frac{1}{12} = \frac{12}{12} = 1 \text{ hour} \]

### Final Answer:
The total time taken to cover the total distance of 20 km is **1 hour**.