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Question

Hi! I need help with the two questions below. Thanks!

a) Xiao Ming and four of his friends were hired for a job. If Xiao Ming got one more friend to join the team, the job can be completed 6 days earlier. Assuming all of them work at the same rate, how many friends should Xiao Ming ask to join the original team so that they can complete the job 12 days earlier?

b) It is given that x is directly proportional to y and y is directly proportional to z. Prove that x + y is directly proportional to z

Answer

b) It is given that x is directly proportional to y and y is directly proportional to z. Prove that x + y is directly proportional to z

Let a and b be 2 constants.

x is directly proportional to y => x = ay

y is directly proportional to z => y = bz

Expressing y in terms of z, we get x = a(bz) = (ab)z

Hence, x + y = (ab)z + bz = (ab+b)z

Since (ab+b) is another constant, we can therefore conclude that x + y is directly proportional to z.

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1) Not sure if my working is correct as the answer is not a whole number.

Amount of work are usually described has ‘man hours’ but in this case I will calculate as ‘man days’

Original team of 5 people took ‘D’ days to complete

Work = 5D man.days

With 6 person, Work = 6(D-6) = 6D-36 man.days

Work done is the same regardless of how many man or days.

5D = 6D-36

D = 36 days

Therefore work = 5D = 180 man.days

Less 12 days, = 36-12= 24

Man required for 24 days= 180/24= 7.5

So he requires an additional of 2.5 friends or round up to 3 friends to guarantee the work to be completed in 12 days earlier.

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