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It takes 10 people 5 days to complete a piece of work at a factory when working 2 hours a day. Working at the same pace, how many days will it take 2 people to do the same work, if they are working 5 hours a day?
Answers
10 people : 5 days : 2 hours a day (Given)
Find the number of days needed if there is only 1 person:
10 people : 5 days : 2 hours a day
10 ÷ 10 people : 5 x 10 days : 2 hours a day
1 person : 50 days : 2 hours a day
Find the number of days needed if there are 2 people:
1 person : 50 days : 2 hours a day
1 x 2 people : 50 ÷ 2 days : 2 hours
2 people : 25 days : 2 hours
Find the number of days needed if they worked 1 hour a day:
2 people : 25 days : 2 hours
2 people : 25 x 2 days : 2 ÷ 2 hours
2 people : 50 days : 1 hours
Find the number of days needed if they worked 5 hours a day:
2 people : 50 days : 1 hours
2 people : 50 ÷ 5days : 1 x 5 hours
2 people : 10 days : 5 hours
Answer: They need 10 days
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ALTERNATIVE METHOD:
The number of people needed is inversely proportional to the number of days
⇒ the more people they have, the fewer days they need to work
10 people → need 5 days
1 person → 5 x 10 = 50 days
2 people → 50 ÷ 2 = 25 days
The number of hours worked in a day is inversely proportional to the number of days they need to work.
⇒ the more hours they worked in a day, the fewer days they need to work
2 hours → needs 25 days
1 hour → 25 x 2 = 50 days
5 hours → 50 ÷ 5 = 10 days
Answer: They need 10 days