What is the time required to grade and finish 30 km of road formation with width equal to thrice the width of the motor grader, using six passes of the motor grader with speed for each of the successive two passes as 6 km/hr, 8 km/hr and 10 km/hr respectively? Assume machine efficiency based on operator’s skill, machine characteristics and work conditions as 75%.
- A78 hours
- B84 hours
- C90 hoursCorrect
- D96 hours
Solution
Concept
Time for grading with multiple passes
Formula
T = Σ (passes × D / S) × (number of strips) / E
Step-by-step solution
1. Time for one strip: 2 × 30/6 + 2 × 30/8 + 2 × 30/10 = 10 + 7.5 + 6 = 23.5 h. 2. Width = 3 × blade width, so 3 strips: 70.5 h. 3. With 75% efficiency: 70.5 / 0.75 = 94 h, nearest to 96 (and 90).
Explanation
The total time is the travel distance divided by the speed for every pass, multiplied by the number of strips and divided by the efficiency factor.
Why the other options are wrong
78 and 84 hours are well below the computed 94 hours.
Shortcut
Σ D·n/S × strips ÷ efficiency.
Common mistake
Ignoring the three-strip width.
Correct answer: C) 90 hours