Question 1198854
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The jump from 6 hours to 3 hours is "times 1/2".


This strongly suggests the two people work at the same rate, and take the same amount of time. 
This is because they split the work in half (thereby cutting their worktime in half as well).


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We can think of it like saying the task is to move 60 bales of hay.
Quiboy needs 6 hours to do the job by himself. 
His unit rate is 60/6 = 10 bales per hour.


When working together, the two men can do the job in 3 hours. 
Their combined rate is 60/3 = 20 bales per hour.
This of course assumes neither worker hinders the other.


Quiboy offers 10 bales per hour, and the total combined rate is 20 bales per hour. 
Rod offers the remaining 20-10 = 10 bales per hour. 
His rate is the same as Quiboy. So he takes the same amount of time.


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If you wish to use algebra, then,
x = time (in hours) needed for Rod to do the job alone


1/6 = Quiboy's unit rate
1/x = Rod's unit rate
1/3 = combined unit rate


1/6 + 1/x = 1/3
x/(6x) + 6/(6x) = 1/3
(x+6)/(6x) = 1/3
3(x+6) = 6x*1
3x+18 = 6x
18 = 6x-3x
18 = 3x
3x = 18
x = 18/3
x = 6


Or you could say
1/6 + 1/x = 1/3
6x * ( 1/6+1/x ) = 6x*( 1/3 )
6x*(1/6) + 6x*(1/x) = 6x*( 1/3 )
x + 6 = 2x
6 = 2x-x
6 = x
x = 6



In my opinion an algebraic approach is a bit overkill. 
Despite that, it's still handy to know this pathway and get practice.


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Answer: 6 hours
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