Question 829618
b = Betty's rate in floors per minute is 1 floor/8 min = 1/8 floor per minute.
n = Nancy's rate
(b+n)6 = 1 floor
( 1/8 + n )6 = 1
 6/8 + 6n = 1
subtract 6/8 from each side
 6n = 1 - 6/8
 6n = 8/8 -6/8
 6n = 2/8
multiply each side by 1/6
 n = (1/6)(2/8)
   = 2/48
 = 1/24
Let's check
(1/8 + 1/24)6 ?= 1
(3/24 + 1/24)6 ?= 1
(4/24)6 ?= 1
(1/6)(6) = 1
So it checks out.
Nancy's rate is 1/24 floor per minute, so she will need 24 minutes to mop
the floor.