how to solve rational problem solving question

Marissa's rate is $frac {1 door}{3 hours}= frac 13frac {door}{hr}$

Rogers rate is unknown. Lets say it is $x frac {door}{hr}$

Together their rate is $(frac 13 + x) frac {door}{hr}$ and that is $frac {1 door}{1 hour} = 1frac {door}{hour}$

So $(frac 13 + x)frac {door}{hr} = 1 frac {door}{hr}$ so

$x = frac 23frac{door}{hr}$ and that is rogers rate; it can point $frac 23$ of a door in an hour or $2$ doors in $3$ hours.

So what was the question again? .... Oh, you.... how long dooes it take Roger to pain a door.

So if that tirme is $t hours$ then Roger paints $frac 23 frac {door}{hr}times t hr = 1 door$.

$require {cancel}$

$frac 23 frac{door}{{hr}}times t {hr} = 1 door$

$t hr = 1 door cdot frac 32 frac {hr}{door} = 1frac 12 hr$.

Roger can paint a door in $1 frac 12$ hours