SOLUTION: hannah can paint a room in 8hrs. Miley can paint it in 10hrs. working together, how many hrs would it take them to paint the room?

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Question 221073: hannah can paint a room in 8hrs. Miley can paint it in 10hrs. working together, how many hrs would it take them to paint the room?
Found 2 solutions by Alan3354, scott8148:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
hannah can paint a room in 8hrs. Miley can paint it in 10hrs. working together, how many hrs would it take them to paint the room?
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Hannah does 1/8 room per hour.
Miley does 1/10 per hour.
Together, they do 1/8 + 1/10 per hour = 9/40 room per hour.
9/40 room/hour --> 40/9 hours/room
40/9 hours = ~ 4.44 hours
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There's a shortcut, product/sum
8*10/(8+10) = 80/18
= 40/9

Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
if T is their combined time, then the FRACTION painted by Hannah is T/8 and the FRACTION painted by Miley is T/10
___ the FRACTIONS add to 1 (the WHOLE room)

T/8 + T/10 = 1

multiplying by 40 (LCD) ___ 5T + 4T = 40 ___ 9T = 40 ___ T = 40/9 (about 4.5 hr)