Two coal loading machines each working 12 hours per day for 8 days handle 9000 tonnes of coal with an efficiency of 90% while 3 other coal loading machines at an efficiency of 80% are set to handle 12000 tonnes of coal in 6 days. Find how many hours per day each should work.
Answer
Answer (as printed):
Explanation
Let the number of working hours per day be x. More machines, Less working hours per day (Indirect Proportion) Less days, More working hours per day (Indirect Proportion) More coal, More working hours per day (Direct Proportion) Less efficiency, More working hours per day (Indirect Proportion) Machines 3:2 Days 6:8 : : 12 : x Coal 9000 : 12000 Efficiency 80 : 90 2 × 8 × 12000 × 90 × 12 \ 3 × 6 × 9000 × 80 × x = 2 × 8 × 12000 × 90 × 12 ⇔ x = = 16. 3 × 6 × 9000 × 80 Hence, each machine should work for 16 hours per day.
Explanation as extracted from the printed page; notation may be imperfect.