If Joanne can paint a room in 5 hours and her sister Angela can paint the same room in 6 hours, how long (in h) would it take Joanne and Angela to paint the room working together?

Answer 1

Joanne paints 1/5 of room in an hour

Angela paints 1/6 of room in an hour

Together they pain 1/5 + 1/6 = 11/30 of room in hour

11/30 job in an hour * x hours = one job

x hours = one job

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11/30 job

= 30/11 hours

Answer 2

If Joanne can paint a room in 5 hours and her sister Angela can paint the same room in 6 hours, how long (in h) would it take Joanne and Angela to paint the room working together?

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This problem is similar to Rate x Time = Distance problems. Rate of Work x Time to Complete = Completed Job

J = rate of painting in 1 hour for Joanne

A = rate of painting in 1 hour for Angela

R = Completed Painted Room

J x 5h = R (1 Painted Room).....in one hour....J does 1/5 painted room....1/5 room in 1 hour (rate of painting)

A x 6h = R (1 Painted Room)....in one hour....A does 1/6 painted room.....1/6 room in 1 hour (rate of painting)

(J+A) x T = R

(1/5 Room/Hour + 1/6 Room/Hour) x T (in Hours) = R

(6/30 R/H + 5/30 R/H) x T = R

11/30 R/H x T = R

T = 30/11 H....approximately 2.72 Hours....Right?