Question

The length of time, y hours, it takes to put a jigsaw puzzle together is inversely proportional to the number of children, x, working on it. It takes 16 children 6 hours to put the jigsaw puzzle together. How many children are needed to put the same jigsaw puzzle together in 4 hours?

Answer 1

24 children

Explanation:

If the length of time, y hours, it takes to put a jigsaw puzzle together is inversely proportional to the number of children, x, this is represented as;

`y \alpha (1)/(x)\\y =(k)/(x)`

k is the constant of proportionality

If it takes 16 children 6 hours to put the jigsaw puzzle together, this means at x = 16, y = 6

Substitute:

6 = k/16

k = 6*16

k = 96

W are to find number of children needed to put the same jigsaw puzzle together in 4 hours, this is done by substituting k = 96 and y = 4 into the expression y = k/x

y = 96/4

y = 24

Hence it will take 24 children to put the same jigsaw puzzle together in 4 hours