Rationals

[Guest]

Johnny and Susie work for Proportions Paint Company. Johnny and Susie are paid per room they paint. Susie can paint a room in 10 hours. Working together they can paint a room in 6 hours.
How long does it take Johnny to paint a room?
Had a hard time with this one, looking for help. Thanks!

[Guest]

In problems like this it is rates that add.

"Susie can paint a room in 10 hours. Working together they can paint a room in 6 hours.
How long does it take Johnny to paint a room?"
Susie's rate is one room in 10 hours or 1/10 room per hour. We want to find Johnny's rate so call that "R". Working together they can paint a room in 6 hours so their rate together is 1/6 room per hour: 1/10+ R= 1/6.

R= 1/6- 1/10.

[HallsofIvy]

This has been here a while and my (hopefully mild) compulsive disorder forces me to finish it!

[tex]R= \frac{1}{6}- \frac{1}{10}= \frac{5}{30}- \frac{3}{30}= \frac{2}{30}= \frac{1}{15}[/tex].

Since "R" is the rate of work, in "rooms per hour" for Johnny, he does 1/15 "room per hour" so 15 "hours per room". It would take Johnny 15 hours to paint one room alone.

(10 hours and 15 hours to paint a single room is awfully slow, isn't it?)