Question

Layna can paint a 350-square foot room in 4 hours. It takes Bebe 7 hours to paint the same room. Which equation can be used to find the time in hours, t, it takes Layna and Bebe to paint the room together?


Rate
(Rooms per Hour)
Time
(Hours)
Fraction Completed
Layna
One-fourth

Bebe
One-seventh

One-fourth t + one-seventh t = 1
One-fourth t times one-seventh t = 1
4 t + 7 t = 1
4 t minus 7 t = 1

Answer 1

This is a little hard to explain without giving away too much, but think of if like this:

Layna takes 4 hours to do the whole job, so she does (1/4) of the job per hour. in (t) hours, Layna paints (1/4)t of the room.
Similar logic with Bebe; he does (1/7) of the job per hour and (1/7)t of the room in (t) hours.

Both people's work can add up to 1 (representing 1 whole job)