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Maths question

Vatour

01 Sep 14 14:35

Joined:

Date Joined: 22 Mar 14

| Topic/replies: 162 | Blogger: Vatour's blog

One day, it takes p hours for q factory workers to construct r items. The following day, three more workers join the team and four more items are required to be constructed.

(i) Find how many hours it will take, in terms of p, q and r.
(ii) If in fact it takes the same length of time, find an equation and show that it reduces to 4q=3r.

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Report PatraTheCat • September 1, 2014 2:47 PM BST

Hours required on second day = p' will be hours (p) worked on first day multiplied by the factor given by the extra workers {(q+3/q)} but divided by the factor given by the extra items that need to be made {(r+4)/r)}.

Therefore p'=p{(q+3)/q)}{r/(r+4)}

If p'=p:

1=1{(q+3)/q)}{r/(r+4)}

So {(q+3)/q}{r/{+4)}=1

So 1+(3/q)=1+(4/r)

So 4q=3r