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Question 254053: Patricia and chelsea can build a bike together in an hour and a half. However, if Patricia worked with Tanesha they can build the same bike 10 minutes faster. Working by herself, Patricia can build a bike 2 hours faster than Tanesha.
a) How long will it take for each girl to build a bike by herself?
b) How long will it take for the three of them to build a bike together
Found 2 solutions by palanisamy, richwmiller:
Answer by palanisamy(496)   (Show Source):
You can put this solution on YOUR website! Let,
Patricia can build the bike alone in x hours.
Chelsea can build the bike alone in y hours.
Tanesha can build the bike alone in x+2 hours
Then,
the work done in one hour by Patricia is 1/x
the work done in one hour by Chelsea is 1/y
the work done in one hour by Tanesha is 1/x+2
Given,
Patricia and chelsea can build a bike together in an hour and a half.
1/x +1/y = 1/(1+1/2)
1/x+1/y = 1/(3/2)
1/x+1/y = 2/3 ...(1)
If Patricia worked with Tanesha they can build the same bike 10 minutes faster
1/x + 1/(x+2) = 1/(1+20/60)
(x+2+x)/x(x+2) = 1/(1+1/3)
(2x+2)/x(x+2) = 1/(4/3)
(2x+2)/x(x+2) = 3/4
4(2x+2)=3x(x+2)
8x+8 = 3x^2+6x
0 = 3x^2+6x-8x-8
3x^2-2x-8 = 0
3x^2-6x+4x-8 = 0
3x(x-2)+4(x-2) = 0
(x-2)(3x+4) = 0
x = 2 or x = -4/3
Since x cannot be negative, we take x = 2
Substituting in (1), we get
1/2 + 1/y = 2/3
1/y = 2/3 - 1/2
1/y = (4-3)/6
1/y = 1/6
y=6
Therefore,
Patricia can build the bike alone in 2 hours
Chelsea can build the bike alone in 6 hours.
Tanesha can build the bike alone in x+2 = 2+2 =4 hours
b) If all of the work together,
1/x+1/y+1/(x+2) = 1/2+1/6+1/4 = (6+2+3)/12 = 11/12 hours
The bike can be built in 11/12 hours = (11/12)*60= 55 minutes
Answer by richwmiller(17219)  (Show Source):
You can put this solution on YOUR website! I like palanisamy's work and answer but the answers don't meet the criteria
The problem states that patricia works 2 hours faster than Tanesha
palanisamy has Patricia done in less than 2 hours but tanesha takes 8 hours
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