# maths, variations

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i'm not sure how this question works

the number of hours (h) taken to paint a picture is inversely proportional to th number of pupils (p) painting it. it takes 4 pupils 3 hours to finish painting it assuming all pupils work at the same rate.

a) find an equation connecting h and p
is this correct? : h=-kp

b) find how much longer it would take if one of the pupils is not painting.
(i'm not sure how to do)

c) find the additional number of pupils required if the painting is to be completed in 2 hours.

i would appreciate if you could explain detailedly with the help of workings! thanks!

• maths, variations -

a) No. h = k/p
3 = k/4
k = 12
h = 12/p

b) Change p from 4 to 3 in the equation aboveand you get
h = 4 hours

c) If you want h to be 2 hours, plug in h =2 in the h=12/p equation and see what you get for p. Subtract 4 from that to get the number of additional pupils

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