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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.

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    $\begingroup$ 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? $\endgroup$
    – Aiden Chow
    Sep 16, 2020 at 20:08
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    $\begingroup$ 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. $\endgroup$
    – lulu
    Sep 16, 2020 at 20:10
  • $\begingroup$ Regardless how you established your equations, it is obvious that the answer must be smaller than 3 (Roger works faster). $\endgroup$
    – user65203
    Sep 16, 2020 at 20:10
  • $\begingroup$ is their a n equation that can represent that ? @lulu $\endgroup$ Sep 16, 2020 at 20:27
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    $\begingroup$ 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? $\endgroup$
    – EuxhenH
    Sep 16, 2020 at 21:06

1 Answer 1

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

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

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

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

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