SOLUTION: David can do a job in 15 days while ken can do the same job in 10 days.If both started the work together and ken quit after 2 days while david finished the job how long will the e

Algebra ->  Test -> SOLUTION: David can do a job in 15 days while ken can do the same job in 10 days.If both started the work together and ken quit after 2 days while david finished the job how long will the e      Log On


   

Question 1036417: David can do a job in 15 days while ken can do the same job in 10 days.If both started the work together and ken quit after 2 days while david finished the job how long will the entire job take?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
David's rate of working:
[ 1 job ] / [ 15 days ]
Ken's rate of working:
[ 1 job ] / [ 10 days ]
---------------------
Add their rates of working to get their
rate working together
+1%2F15+%2B+1%2F10+=+2%2F30+%2B+3%2F30+
+2%2F30+%2B+3%2F30+=+5%2F30+
+5%2F30+=+1%2F6+
------------------
Their rate working together is:
[ 1 job ] / [ 6 days ]
------------------
In 2 days, the fraction of the job completed is
+2%2A%28+1%2F6+%29+=+1%2F3+
That means there is +2%2F3+ of the job left
after 2 days
-------------------------------------
Ken leaves after 2 days.
Let +t+ = time in days for David to finish the job
+1%2F15+=+%28%28+2%2F3+%29%29+%2F+t+
+1%2F15+=+2%2F%28+3t+%29+
Multiply both sides by +15t+
+t+=+10+
David takes 10 days to finish the job
+2+%2B+10+=+12+
The entire job takes 12 days to finish