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!
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
a) To find the equation connecting h and p, we can use the idea of inverse proportionality. Inverse proportionality means that as one variable increases, the other variable decreases, while their product remains constant.
We are given that when there are 4 pupils (p = 4), it takes 3 hours (h = 3) to finish painting. So, we can write their product as constant:
h * p = k
Substituting the values, we get:
3 * 4 = k
12 = k
Therefore, the equation connecting h and p is:
h * p = 12
b) To find how much longer it would take if one of the pupils is not painting, we need to consider the new value of p.
Since one pupil is not painting, the new value of p would be 3 (original value of p = 4 - 1). We want to find the new value of h.
Using the equation h * p = 12, we can substitute the new value of p and solve for h:
h * 3 = 12
h = 12 / 3
h = 4
Therefore, it would take 4 hours to finish painting if one of the pupils is not painting, which is 1 hour longer than before.
c) To find the additional number of pupils required if the painting is to be completed in 2 hours, we need to consider the new value of h.
Since we want to complete the painting in 2 hours, we substitute h = 2 into the equation h * p = 12 and solve for p:
2 * p = 12
p = 12 / 2
p = 6
Therefore, an additional 2 pupils (original value of p = 4) are required to complete the painting in 2 hours.