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.

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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