how to solve rational problem solving question

Question

Marissa can paint a garage door in $3$ hours. When Marissa works with Roger, they can paint the same door in $1$ hour. How long would it take Roger to paint the door on his own(answer to the nearest tenth)?

My work

Marissa paints a garage door in $3$ hours
$\text{Marissa}+\text{Roger}=1$ hour
How long will it take roger$=x$

$x+3/x+1+x/x=$
It takes Roger $3.3$ hours.

Answer 1

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

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 $\frac {1 door}{1 hour} = 1\frac {door}{hour}$

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

$x = \frac 23\frac{door}{hr}$ 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 $\frac 23 \frac {door}{hr}\times t\ hr = 1\ door$.

$\require {cancel}$

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

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

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