6 men take 10 days to paint an apartment. Calculate the number of men required to paint the same apartment in 3 days. Answer ... The braking distance, $d$ of a car is directly proportional to the square of its speed, $v$. When the speed of the car is increased by 200%, find the percentage increase in its braking distance. Answer ... %

1. Find the number of men needed for 3 days using constant man-days.

For the same apartment,
$6 \times 10 = x \times 3$
$x=\frac{6\times 10}{3}=20$

1. Express the new speed after a 200% increase.

A 200% increase means the new speed is
$v+200\%\text{ of }v= v+2v=3v.$

2. Use $d\propto v^2$ to find the percentage increase in braking distance.

Since $d\propto v^2$,
$\frac{\text{new }d}{\text{original }d}=\frac{(3v)^2}{v^2}=9.$
So the new braking distance is $900\%$ of the original.

Percentage increase
$=900\%-100\%=800\%.$