# Jake, Lionel, and Wayne work as house painters for Paint Well Company. Jake can paint 1 room in t hours. Lionel can paint a room 2 hours faster than Jake can. Wayne can paint 2 rooms in 3 times the number of hours that Lionel takes to paint 1 room?

Oct 30, 2016

$\frac{12}{7}$ hours to paint 1 room if they all work together

#### Explanation:

color(red)("You have defined the work rate but not stated the number of rooms"
color(red)("to be painted. I will work this out for 1 room and you will have to"
$\textcolor{red}{\text{proportion this up (or down) for however many rooms are needed.}}$

For 1 room only:

Jake $\to 1 \times t \text{ room hours}$

Lional$\to 1 \times \left(t - 2\right) \text{ room hours}$

Wayne$\to 1 \times \frac{3 \left(t - 2\right)}{2} \text{ room hours "larr" 2 rooms in } 3 \left(t - 2\right)$

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$\textcolor{b l u e}{\text{Determine the time for 1 room if they all work together}}$

$t + \left(t - 2\right) + \frac{3 \left(t - 2\right)}{2} = 1$

$t + t + \frac{3}{2} t - 2 - \frac{6}{2} = 1$

$\frac{7}{2} t = 1 + 2 + 3$

$t = \frac{2 \times 6}{7} \text{ hours}$

$t = \frac{12}{7} \text{ hours"larr" For 1 room}$