Question

Carla wraps the utensils in a cloth napkin for a party three times as fast than Karen does. Together they need to organize 90 napkins in three hours. How many hours will it take each of them if they are working alone?

Answer 1

Let x be the number of napkins Carla organized in 1 hour, and y be the number of napkins Karen organized in 1 hour, then we can set the following system of equations:

$\begin{gathered} 3x+3y=90, \\ x=3y\text{.} \end{gathered}$

Substituting x=3y in the first equation we get:

$3(3y)+3y=90.$

Solving for y we get:

$\begin{gathered} 9y+3y=90, \\ 12y=90, \\ y=\frac{90}{12}, \\ y=7.5. \end{gathered}$

Therefore, Karen organized 7.5 napkins each hour and Carla organized 7.5x3=22.5 napkins each hour.

Answer: Since Karen organized 7.5 napkins each hour, then it would take her

$\frac{90}{7.5}=12$

hours to do the 90 napkins.

Since Carla organized 22.5 napkins each hour, it would take her

$\frac{90}{22.5}=4$

hours to do the 90 napkins.