The air resistance, $R$ newtons, is directly proportional to the square of the speed, $V$ m/s, of an object when it is falling.
The air resistance is 24 newtons at a certain speed.
Find the air resistance when the speed is increased by 50%. Answer ___ newtons 16 workers can tile 2 rooms in 60 hours.
How many workers are needed if 5 rooms are to be tiled in 72 hours? Answer ___ workers

1. Represent the 50% increase in speed as a scale factor.

A 50% increase means the new speed is
$100\%+50\%=150\%=1.5$
of the original speed.

2. Apply the square relationship between air resistance and speed.

Since $R$ is directly proportional to $V^2$,
$R \propto V^2.$
When $V$ is multiplied by $1.5$, $V^2$ is multiplied by
$(1.5)^2=2.25.$

3. Find the new air resistance.

Original air resistance $=24$ N.
$\text{New air resistance}=24\times 2.25=54$

1. Set up the worker scaling using rooms and hours.

For the same tiling rate per worker,
$\text{workers} \propto \frac{\text{rooms}}{\text{hours}}.$
So
$W=16\times \frac{5}{2}\times \frac{60}{72}.$

2. Calculate the required number of workers.

$W=16\times \frac{5}{2}\times \frac{60}{72}=16\times \frac{5}{2}\times \frac{5}{6}=\frac{200}{6}\times 5?$
More directly,
$W=16\times \frac{5}{2}\times \frac{60}{72}=16\times 2.5\times \frac{5}{6}=40\times \frac{5}{6}=\frac{100}{3}.$