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Question: 6 people can do a job in 10 hours. How long will it take 9 people to do the same job?


A ) 15 hours
B ) 5 hours 24 minutes
C ) 6 hours 40 minutes
D ) 6 hours

Steps to derive

1 Let the time taken to do a job be t and the number of people be n.

1 Let the time taken to do a job be t and the number of people be n.

2 The time taken to do a job varies inversely as the number of people.
      t = kn

2 The time taken to do a job varies inversely as the number of people.
      t = kn

3 Substitute the values of t and n to find k.
    10 = k6
    k = (10)(6) = 60

3 Substitute the values of t and n to find k.
    10 = k6
    k = (10)(6) = 60

4 So, the equation of variation is, t = 60n

4 So, the equation of variation is, t = 60n

5 To find the time taken by 9 people, substitute 9 for n in the equation.
t = 609 = 6 hours 40 minutes

5 To find the time taken by 9 people, substitute 9 for n in the equation.
t = 609 = 6 hours 40 minutes

6 9 people can do the same job in 6 hours 40 minutes.

6 9 people can do the same job in 6 hours 40 minutes.



Hence the right answer is Option C

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