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Question 920853: I'm trying to help my nephew with algebra... it's been a while.
1. Brooks can mow the lawn twice as fast as his sister Katrina. Together they can do the job in 2.5 hours. How long would it take each of them working alone?
2. It takes 5 hours for Lena to paint a room. It takes 3 hours for Lena and Gustov together to paint the same room. How long would it take Gustov alone to paint the room?
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! 1) let 2x be the time Katrina mows the lawn, then
1/x + 1/2x = 1/2.5
2.5x is GCD
2.5 + 2.5/2 = x
multiply both sides of = by 2
5 + 2.5 = 2x
so 2x = 7.5 hours for Katrina to mow lawn, therefore
x = 3.75 hours for Brooks to mow lawn
2) let x be time for Gustov to paint room, then
1/x + 1/5 = 1/3
15x is GCD
15 + 3x = 5x
15 = 2x
x = 7.5 hours for Gustov to paint the room
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