A bulldozer operates on a 30 m stretch and moves at 2.4 kmph when pushing the earth, and returns empty at 6 kmph. The time lost in loading and shifting gears per trip is 18 seconds. Its operating factor is nearly 50 min/hour. What is the number of trips made per hour?
- A31
- B33
- C35
- D37Correct
Solution
Concept
Bulldozer Production and Cycle Time
Formula
Number of Trips per Hour = Operating Time per Hour / Total Cycle Time per Trip
Step-by-step solution
1. Calculate forward travel time: 30 m / (2.4 × 1000/3600 m/s) = 45 seconds. 2. Calculate return travel time: 30 m / (6 × 1000/3600 m/s) = 18 seconds. 3. Calculate total cycle time per trip: 45 s + 18 s + 18 s (lost time) = 81 seconds. 4. Convert operating factor to seconds: 50 minutes × 60 = 3000 seconds. 5. Divide operating time by total cycle time: 3000 / 81 ≈ 37 trips per hour.
Explanation
1. Forward time = Distance / Forward speed = 30 m / (2.4 × 1000/3600 m/s) = 45 seconds. 2. Return time = Distance / Return speed = 30 m / (6 × 1000/3600 m/s) = 18 seconds. 3. Time lost per trip = 18 seconds. 4. Total cycle time per trip = 45 + 18 + 18 = 81 seconds. 5. Operating time per hour = 50 minutes = 3000 seconds. 6. Number of trips per hour = 3000 / 81 ≈ 37 trips.Therefore, Option D (37) is correct.
Shortcut
Convert speeds directly to time using 3.6 × Distance / Speed in km/h. Forward time = 3.6 × 30 / 2.4 = 45 s; Return time = 3.6 × 30 / 6 = 18 s. Add lost time (18 s) to get total cycle time = 81 s. Finally, divide available operating seconds (50 × 60 = 3000 s) by 81 s to get approximately 37 trips.
Common mistake
A common mistake is using 60 minutes (3600 seconds) instead of the 50-minute operating factor (3000 seconds) when calculating trips per hour, or forgetting to add the 18-second fixed time delay (loading and gear shifting) to the total cycle time.
Correct answer: D) 37