Question

A lifeguard fills a pool with water at a constant rate. After 12 hour, 13 of the pool is filled. At this rate, what fraction of the pool is filled per hour?.

Answer 1

At the considered rate the fraction of pool that is filled per hour is 13/12

How to measure the rate of change of something as some other value changes?

Suppose that we have to measure the rate of change of y as x changes, then we have:

$Rate = \dfrac{y_2 - y_1}{x_2 - x_1}$

where we have

$\rm when \: x=x_1, y = y_1\\when\: x = x_2, y= y_2$

Remember that, we divide by the change in independent variable so that we get some idea of how much the dependent quantity changes as we change the independent quantity by 1 unit.

(5 change per 3 unit can be rewritten as 5/3 change per 1 unit)

For the considered case, we can take time spent as difference of independent variable, and the amount of pools filled as the corresponding difference of the dependent variable.

in 12 hour time interval total 13 pools were filled.

That means

Rate of filling the pool is 13 pools per 12 hours or $\dfrac{13}{12}$ pools per hour.

Thus, at the considered rate the fraction of pool that is filled per hour is 13/12

Learn more about rate of change here:

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