There are three trucks A, B, C. A loads 10 kg/min. B loads 13⅓ kg/min. C…
2023
There are three trucks A, B, C. A loads 10 kg/min. B loads 13⅓ kg/min. C unloads 5 kg/min. If all three work simultaneously, what is the time taken to load 2.4 tonnes?
- A.
3 hrs 10 min
- B.
2 hrs 10 min
- C.
4 hrs 20 min
- D.
6 hrs 11 min
Attempted by 35 students.
Show answer & explanation
Correct answer: B
Step 1: Convert rates to kg/min: A = 10 kg/min; B = 13 1/3 kg/min = 40/3 kg/min; C unloads 5 kg/min (subtract).
Step 2: Net rate:
Net = 10 + 40/3 − 5 = (30 + 40 − 15)/3 = 55/3 kg/min ≈ 18.333... kg/min.
Step 3: Time to load 2.4 tonnes (2400 kg):
Time = 2400 ÷ (55/3) = 2400 × 3/55 = 7200/55 = 1440/11 minutes ≈ 130.909... minutes.
Convert to hours and minutes: 130.909... minutes = 2 hours + 10.909... minutes = 2 hours 10 minutes 54.5 seconds (approximately).
Conclusion: The exact time is 1440/11 minutes (≈ 2 hr 10 min 55 s). The closest answer among the choices is the one that states "2 hrs 10 min" (note that if rounding to the nearest minute, the time would be 2 hrs 11 min).