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)?

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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