# If it took Jane 3/4 hour by long will it take to paint a wall that was 12 ft by 12 ft, how long will it take to paint another wall that is 15 ft by 16 ft?

Feb 2, 2018

$\frac{5}{4}$ $\text{h}$

#### Explanation:

The idea here is that you need to figure out how much time is needed to paint ${\text{1 ft}}^{2}$ knowing that it takes $\frac{3}{4}$ of an hour to paint a wall that has a total area of

${\text{12 ft" xx "12 ft" = "144 ft}}^{2}$

This is the case because the area of a rectangle--or a square, like you have in this case--is calculated by multiplying the length and the width of the rectangle.

So, you know that Jane needs $\frac{3}{4}$ of an hour to paint ${\text{144 ft}}^{2}$, which means that she paints ${\text{1 ft}}^{2}$ in

1 color(red)(cancel(color(black)("ft"^2))) * (3/4 quad "h")/(144color(red)(cancel(color(black)("ft"^2)))) = 1/192 quad "h"

Now, the area of the second wall is equal to

${\text{16 ft" xx "15 ft" = "240 ft}}^{2}$

This means that Jane will paint this wall in

240 color(red)(cancel(color(black)("ft"^2))) * (1/192 quad "h")/(1color(red)(cancel(color(black)("ft"^2)))) = 5/4 quad "h" = "1.25 h"

You can thus say that Jane will need $1.25$ hours, or $1$ hour and $15$ minutes--remember that $1$ hour has $60$ minutes--to paint the second wall.