9th algebra
posted by Summer on .
1.Jeff can weed the garden in 4 h. His wife takes the same amount of time. After they worked for 1 hr, their son helped them finish in 1/2 h. H long would it have taken Rory by himself to weed the garden?

jeff's rate = 1/4
wife's rate = 1/4
combined rate = 1/4 + 1/4 = 1/2
job done after 1 hr = (1/2)(1 hr) = 1/2
let son's rate be 1/x , (who is Rory ? )
combined rate = 1/4 + 1/4 + 1/x
= 1/2 + 1/x
= (x+1)/(2x)
time for rest of job = (1/2)/combined rate)
(1/2)/((x+1)/(2x))
= (1/2)(2x/(x+1)
= x/(x+1)
but x/(x+1) = 1/2 hr
2x = x+1
x = 1
So Rory could do the garden in 1 hour by himself 
eh?
mom and pop each do 1/4 job in 1 hour
so, 1/2 job remained when Rory came to work.
In the next 1/2 hour, mom and pop each did another 1/8 of the job, or 1/4 combined.
That left 1/4 of the job for Rory to do in 1/2 hour. So, Rory could do the whole job in 2 hours by himself.