Question

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?

Answer 1

`5/4` `"h"`

Explanation:

The idea here is that you need to figure out how much time is needed to paint `"1 ft"^2` knowing that it takes `3/4` of an hour to paint a wall that has a total area of

`"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 `3/4` of an hour to paint `"144 ft"^2`, which means that she paints `"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

`"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.