# how to solve rational problem solving question

Mathematics Asked by Ranveer Masuta on September 29, 2020

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.

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

Answered by fleablood on September 29, 2020

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