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10 4 people take 3 hours to paint a fence - OCR - GCSE Maths - Question 10 - 2018 - Paper 1
Question 10
10 4 people take 3 hours to paint a fence. Assume that all people paint at the same rate. (a) How long would it take one of these people to paint the same fence? (... show full transcript
Worked Solution & Example Answer:10 4 people take 3 hours to paint a fence - OCR - GCSE Maths - Question 10 - 2018 - Paper 1
Step 1
How long would it take one of these people to paint the same fence?
Answer
To find out how long it would take one person to paint the fence, we first need to determine the work rate for one person. If 4 people can paint the fence in 3 hours, then the total amount of work can be understood as follows:
Total work = Number of people × Time = 4 people × 3 hours = 12 person-hours.
Since this work is done by one person, it will take:
Time for one person = Total work / Number of people = 12 person-hours / 1 person = 12 hours.
Thus, it would take one person 12 hours to paint the same fence.
Step 2
How long would it take 5 people to paint the same fence?
Answer
To calculate how long it would take 5 people, we can again refer to the total work of painting the fence which is 12 person-hours. Therefore, the time taken by 5 people can be computed as follows:
Time for 5 people = Total work / Number of people = 12 person-hours / 5 people = 2.4 hours.
To convert 2.4 hours into hours and minutes, we multiply 0.4 hours by 60 minutes:
0.4 hours × 60 minutes/hour = 24 minutes.
Thus, it would take 5 people 2 hours and 24 minutes to paint the same fence.