Question

the number of hours ,h, it takes to wash c number of cars at a school fundraiser is inversely proportional to the number of students ,s, needed to wash the cars. write an equation to represent his relationship

Answer 1

From the given information it is clear that the amount of time, or in other words the number of hours, $h$, required to wash $c$ number of cars are related such that more the number of cars then more is the number of hours to wash those cars.

Thus, we have a relationship between $h$ and $c$ as:

$h\propto c$ .................(relationship 1)

Now, we know that the number of hours is inversely proportional to the number of students. Thus we have:

$h\propto \frac{1}{s}$ .................(relationship 2)

Thus combining the two relationships, (relationship 1) and (relationship 2), we get:

$h\propto \frac{c}{s}$

This is the complete relationship between all the three variables involved.

This can be converted into an equation by replacing the proportionality sign by the equal to sign and constant of proportionality (say $K$) as:

$h=K\frac{c}{s}$