Question

Working together, Rocco and Giulia can paint a room in 3 hours. It would have taken Rocco 7 hours to do the job alone. Which equation can be used to determine r, Giulia’s rate of work in parts per hour?

Answer 1

let complete work of painting be W

In 7 hours , work done by Rocco = W

so in 1 hour , work done by Rocco = W/7

When Rocco and Giulia work together

In 3 hours , work done by Rocco and Giulia = W

in 1 hour , work done by Rocco and Giulia =  W/3

let R by the work done by Giulia's in 1 hour.

So work done by Giulia's in 1 hour + work done by Rocco in 1  = work done by Rocco and Giulia's

⇒ R + W/7 = W/3

⇒ R = W/3 - W/7 = (7W-3W)/21 = 4W/21

So Giulia's rate r can be represented by

r = 4W/21 that is Giulia's completes 4/21 part of work in one hour.