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Question 172347: brother can do the job in "x" hours and sister can do the job in "y" hours. if it takes them 4 hours to do the job working together, then what is the value of "y" ( multiple answers required. assume " x" and "y" are whole numbers) i tried x+y=4 and y= -x+4
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website!
Brother works at the rate of 1/x of the job per hour
Sister works at the rate of 1/y of the job per hour
Together they work at the rate of 1/4 of the job per hour
So we have:
1/x +1/y = 1/4 multiply each term by 4xy
4y+4x=xy
subtract 4y from each side
4y-4y+4x=xy-4y
4x=y(x-4)
solve for y
y=4x/(x-4)
Not only do x and y need to be whole numbers, they also need to be positive numbers; that means that x cannot be 1, 2, 3 otherwise we have a negative values for y. Also, x cannot be 4.
Now we simply start assigning values for x>4 and see what we get:
x=5, y=20
ck
1/5+1/20=1/4
4/20+1/20=1/4
1/4=1/4
x=6, y=12
ck
1/6+1/12=1/4
2/12+1/12=1/4
1/4=1/4
You can carry on from here
Hope this helps---ptaylor
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