Q:

One of Maria and Josie’s early tasks is printing and laminating signs to hang at local businesses around town. Working alone, Maria could print and laminate the signs in 4 hours. Josie, however, has better laminating equipment, so she could get the job done by herself in 2 hours. If each works for the same amount of time, how long will it take them working together to print and laminate the signs? Start by filling in the table with the missing values or expressions. Note that rate of work is a unit rate that describes the amount of the job completed in one hour.

Accepted Solution

A:
Answer:Maria and Josie working together can complete the work in= 1 hour and 20 minutesStep-by-step explanation:Given:Time taken by Maria to print and laminate signs = 4 hoursTime taken by Josie to print and laminate signs = 2 hoursSolution:Rate of work done by Maria = [tex]\frac{1}{4}[/tex] per hourRate of work done by Josie = [tex]\frac{1}{2}[/tex] per hourLet them work for [tex]x[/tex] hours together.In [tex]x[/tex] hours work done by Maria = [tex]\frac{x}{4}[/tex] In [tex]x[/tex] hours work done by Josie = [tex]\frac{x}{2}[/tex]Total work done by both =  [tex]\frac{x}{4}+\frac{x}{2}=\frac{3x}{4}[/tex]If they complete the work in [tex]x[/tex] hours, then we can write as:[tex]\frac{3x}{4}=1[/tex]Solving for [tex]x[/tex]Multiplying both sides by [tex]\frac{4}{3}[/tex][tex]\frac{4}{3}\times\frac{3x}{4}=1\times \frac{4}{3}[/tex]∴ [tex]x=\frac{4}{3}=1\frac{1}{3}[/tex] hours = 1 hour and 20 minutes [As [tex]\frac{1}{3}[/tex] of an hour =20 minutes.So, Maria and Josie working together can complete the work in= 1 hour and 20 minutes