SOLUTION: (7.7 #15) Can someone please help me with this? It takes the owner/operator of a dog kennel 7 hours to clean all of the cages. It takes his assistant 4 hour(s) more than that

Algebra ->  Rate-of-work-word-problems -> SOLUTION: (7.7 #15) Can someone please help me with this? It takes the owner/operator of a dog kennel 7 hours to clean all of the cages. It takes his assistant 4 hour(s) more than that      Log On


   



Question 230944: (7.7 #15)
Can someone please help me with this?
It takes the owner/operator of a dog kennel 7 hours to clean all of the cages. It takes his assistant 4 hour(s) more than that to clean the same cages. How long will it take if they work together?
Thank you,
Daniel

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
What you need to do is to add together
their rates of working to get their rate
working together
In words:
Owner's rate = (all the cages)/(7 hours)
Assistant's rate = (all the cages)/(11 hours)
Let x = their time working together
Call all the cages cleaned 1 job, so
1%2F7+%2B+1%2F11+=+1%2Fx
Multiply both sides by 77x
11x+%2B+7x+=+77
18x+=+77
x+=+4.278 hrs
It takes them 4 hrs 16 min and 40 sec working together
check:
1%2F7+%2B+1%2F11+=+1%2Fx
1%2F7+%2B+1%2F11+=+1%2F4.278
.14286+%2B+.09091+=+.233766
.233769+=+.233766 close enough