# how to solve rational problem solving 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.

• I can't really understand your work. Could you explain how you get the equation $x+3/x+1+x/x$, and what it represents? Sep 16, 2020 at 20:08
• Some commonsense: If $M$ and $R$ both take $3$ hours on their own, it would take them $1.5$ hours working together (since each can do half in $1.5$ hours). So if $R$ takes longer than $3$ hours on his own, they will take longer than $1.5$ hours working together, so $3.3$ can not be right.
– lulu
Sep 16, 2020 at 20:10
• Regardless how you established your equations, it is obvious that the answer must be smaller than 3 (Roger works faster).
– user65203
Sep 16, 2020 at 20:10
• is their a n equation that can represent that ? @lulu Sep 16, 2020 at 20:27
• To get an equation think how much work is being done in 1 hour by each. Marissa is doing $1/3$ of the work in 1 hour, and Roger is doing $1/x$ of the work in 1 hour. What should $1/3 + 1/x$ be? Sep 16, 2020 at 21:06

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