Answer:
Maria and Josie working together can complete the work in= 1 hour and 20 minutes
Step-by-step explanation:
Given:
Time taken by Maria to print and laminate signs = 4 hours
Time taken by Josie to print and laminate signs = 2 hours
Solution:
Rate of work done by Maria =
per hour
Rate of work done by Josie =
per hour
Let them work for
hours together.
In
hours work done by Maria =
In
hours work done by Josie = ![\frac{x}{2}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B2%7D)
Total work done by both = ![\frac{x}{4}+\frac{x}{2}=\frac{3x}{4}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B4%7D%2B%5Cfrac%7Bx%7D%7B2%7D%3D%5Cfrac%7B3x%7D%7B4%7D)
If they complete the work in
hours, then we can write as:
![\frac{3x}{4}=1](https://tex.z-dn.net/?f=%5Cfrac%7B3x%7D%7B4%7D%3D1)
Solving for ![x](https://tex.z-dn.net/?f=x)
Multiplying both sides by ![\frac{4}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B3%7D)
![\frac{4}{3}\times\frac{3x}{4}=1\times \frac{4}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B3%7D%5Ctimes%5Cfrac%7B3x%7D%7B4%7D%3D1%5Ctimes%20%5Cfrac%7B4%7D%7B3%7D)
∴
hours = 1 hour and 20 minutes [As
of an hour =20 minutes.
So, Maria and Josie working together can complete the work in= 1 hour and 20 minutes