
Calculate the time required to grade and finish 30 Km of road formation of 9.0 m width for two-lane
road with motor-grader having a width of 3.0 m, using six passes with speed for each of the successive two passes as 5kmph, 7Kmph and 9 kmph respectively. Assume machine efficiency bases on operator
skill, machine characteristic and working conditions as 80%.
a. Calculate the total area in (km^2) ?
b. Time required in first two pass (hours)?
c. Time require in the consecutive next two pass (hours)?
d. Time require in last two pass(hours)?
e. Total time require considering 80% efficiency (hours)?

Let's go step by step to solve this problem.

### Given Data:

- **Length of road (L)** = 30 km
- **Width of road (W)** = 9 m
- **Motor-grader width** = 3 m
- **Speed for first two passes** = 5 km/h
- **Speed for the next two passes** = 7 km/h
- **Speed for the last two passes** = 9 km/h
- **Efficiency** = 80%

### a. Calculate the total area in \( km^2 \)

The **total area (A)** to be graded is calculated as:
\[
A = \text{Length} \times \text{Width}
\]

Converting the width of the road to kilometers:

\[
\text{Width in km} = 9\, m = 9 \times 10^{-3}\, km
\]

Thus, the area is:

\[
A = 30\, \text{km} \times 9 \times 10^{-3}\, \text{km} = 0.27\, km^2
\]

So, the total area is **0.27 km²**.

---

### b. Time required for the first two passes (hours)

Each pass covers a width of 3 m, so for two passes:

\[
\text{Width covered in two passes} = 3\, m \times 2 = 6\, m
\]

Thus, the length of the road to be covered remains 30 km, but the width is now 6 m (or 6 × 10⁻³ km).

The formula for time is:

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

For the first two passes:

\[
\text{Time for first two passes} = \frac{30 \times 6 \times 10^{-3}}{5} = 0.036\, \text{hours}
\]

For the second pass at 5 km/h:

We will

Calculate the time required to grade and finish 30 Km of road formation of 9.0 m width for two-lane road with motor-grader having a width of 3.0 m, using six passes with speed for each of the successive two passes as 5kmph, 7Kmph and 9 kmph respectively. Assume machine efficiency based on operator skill, machine characteristic and working conditions as 80%. a. Calculate the total area in (km^2)? b. Time required in first two pass (hours)? c. Time required in the consecutive next two pass (hours)? d. Time required in last two pass (hours)? e. Total time required considering 80% efficiency (hours)?

This problem explores the calculation of time required to grade 30 km of road with a motor-grader across six passes at different speeds. It covers key concepts like area calculation, speed-time relations, and efficiency adjustments for machine operation. A detailed step-by-step solution is provided for engineering students.

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