Three printing machines, working together, can print an order of books in 5 hours. The first machine alone would take 10 hours and the second alone would take 30 hours. How many hours would the third machine alone take to print the order?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 15
The joint rate is the sum of the three rates, so the third machine’s rate is the joint rate minus the other two.
All three in an hour: \(\frac{1}{5}\) of the order
Third machine in an hour \(\displaystyle =\frac{1}{5}-\frac{1}{10}-\frac{1}{30}=\frac{6-3-1}{30}=\frac{2}{30}=\frac{1}{15}\)
The third machine alone would take 15 hours.
Why the other options are incorrect
Option (1) 12 — Incorrect. Then the three together would do \(\frac{1}{10}+\frac{1}{30}+\frac{1}{12}=\frac{13}{60}\) an hour, faster than 5 hours.
Option (3) 20 — Incorrect. Then together they would do \(\frac{11}{60}\) an hour and need more than 5 hours.
Option (4) 25 — Incorrect. Then together they would do \(\frac{1}{10}+\frac{1}{30}+\frac{1}{25}\), less than \(\frac{1}{5}\).