### Home > PC3 > Chapter 3 > Lesson 3.2.3 > Problem3-128

3-128.

A rodent got into Barndale’s Department Store and chewed right through one of the store displays. Sidney and her manager Eloise need to work together to build a new display. When Sidney works alone she can build the display in $7$ hours. When Eloise works alone it takes her $5$ hours. How much time will it take to build the new display if Eloise and Sidney work together?

Sidney's rate is $1\;\text{job/7 hours}$.
Eloise's rate is $1\;\text{job/5 hours}$.

Let $t=\text{time}$ to complete the job working together in hours. Then: $\frac{1}{7}t+\frac{1}{5}t=1$
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