SOLUTION: Betty can mop the floor in 8 minutes. Together Betty and Nancy can mop the floor in just 6 minutes. How long does it take Nancy to mop the floor alone?

Question 829618: Betty can mop the floor in 8 minutes. Together Betty and Nancy can mop the floor in just 6 minutes. How long does it take Nancy to mop the floor alone?

Answer by LinnW(1048) (Show Source): You can put this solution on YOUR website!
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.
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