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?

A table showing Rate in part per hour, Time in hours, and Part of Room Painted. The first row shows Rocco and has StartFraction 1 Over 7 EndFraction, 3, and StartFraction 3 Over 7 EndFraction t. The second row shows Giulia, and has r, 3, and 3 r.

+ 3r = 7
+ 3r = 1
= r
= 3r

Answer 1

Use total work = 1. Rocco does 3/7 and Giulia does 3r, so

3/7 + 3r = 1.

Solving gives 3r = 4/7, so r = 4/21 (rooms per hour).