SOLUTION: Jeff can weed the garden in 4 h. His wife Brenda takes the same amount of time. After they worked together for 1 h, their son Rory helped them finish in ½ h. How long would it ha

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Jeff can weed the garden in 4 h. His wife Brenda takes the same amount of time. After they worked together for 1 h, their son Rory helped them finish in ½ h. How long would it ha      Log On


   

Question 610660: Jeff can weed the garden in 4 h. His wife Brenda takes the same amount of time. After
they worked together for 1 h, their son Rory helped them finish in ½ h. How long would
it have taken Rory by himself?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
First find out what fraction of the job Jeff
and his Wife did by themselves
Add their rates of working to get their rate
working together.
( 1 garden/ 4 hrs ) + ( 1 garden / 4 hrs ) = x / 1
Where x is the fraction of the job they do in 1 hr
+1%2F4+%2B+1%2F4+=+x%2F1+
+x+=+2%2F4+
+x+=+1%2F2+
So, they get 1/2 of the job done in 1 hr
There is 1/2 the job left to be done. Then Rory joins them
for 1/2 hr
Add all their rates of working
+1%2F4+%2B+1%2F4+%2B+R+=+1%2F%28+1+%2B+1%2F2+%29+
Where +R+ is Rory's rate of working
+1%2F2+%2B+R+=+1%2F%28%283%2F2%29%29+
+1%2F2+%2B+R+=+2%2F3+
+R+=+2%2F3+-+1%2F2+
+R+=+4%2F6+-+3%2F6+
+R+=+1%2F6+
So, Rory can do ( 1 job ) / ( 6 hrs )
So, he can get the whole job done by himself
in 6 hrs.
------------
check:
+1%2F2+%2B+R+=+1%2F%28%283%2F2%29%29+
+1%2F2+%2B+1%2F6+=+2%2F3+
+3%2F6+%2B+1%2F6+=+4%2F6+
+4%2F6+=+4%2F6+
OK