SOLUTION: please help me solve this problem Two people could finish laying a hardwood floor in seven hours. If the first could do it alone in ten hours, how long could the other person do

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Question 864355: please help me solve this problem
Two people could finish laying a hardwood floor in seven hours. If the first could do it alone in ten hours, how long could the other person do it alone?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x = time it takes for person A to do the job alone
y = time it takes for person B to do the job alone
z = time it takes for them to get the job done when they work together


When we make those definitions above, it turns out that we can tie x,y,z together with this equation

1%2Fx+%2B+1%2Fy+=+1%2Fz


In this case,


x = 10
y = unknown (leave it as y for now)
z = 7


Plug those into the equation and solve for y


1%2Fx+%2B+1%2Fy+=+1%2Fz


1%2F10+%2B+1%2Fy+=+1%2F7


1%2Fy+=+1%2F7-1%2F10


1%2Fy+=+10%2F70-1%2F10


1%2Fy+=+10%2F70-7%2F70


1%2Fy+=+%2810-7%29%2F70


1%2Fy+=+3%2F70


1%2A70+=+3y


70+=+3y


70%2F3+=+y


y+=+70%2F3


So it will take highlight%2870%2F3%29 hours for the second person to do the job alone.


Since 70%2F3+=+23+%26+1%2F3, this means it takes highlight%2823%261%2F3%29 hours (highlight%2823%261%2F3%29 hours = 23 hours, 20 minutes)


If you want the time in minutes only, then multiply it by 60 to get %2870%2F3%29%2A60+=+4200%2F3+=+1400 minutes