SOLUTION: Peter can do a piece of work in 8 days, sam in 10 days and john in 16 days. Sam and john work together for 4 days and then john is replaced by peter. Find when the work will be fin

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Peter can do a piece of work in 8 days, sam in 10 days and john in 16 days. Sam and john work together for 4 days and then john is replaced by peter. Find when the work will be fin      Log On


   

Question 1025939: Peter can do a piece of work in 8 days, sam in 10 days and john in 16 days. Sam and john work together for 4 days and then john is replaced by peter. Find when the work will be finished.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Peter's rate:
[ 1 job done ] / [ 8 days ]
Sam's rate:
[ 1 job done ] / [ 10 days ]
John's rate:
[ 1 job done ] / [ 16 days ]
----------------------
Let +x+ = the fraction of the job that
Sam and John get done in +4+ days
---------
Add their rates of working to get their
rate working together
+1%2F10+%2B+1%2F16+=+x%2F4+
Multiply both sides by +2+
+1%2F5+%2B+1%2F8+=+x%2F2+
Multiply both sides by +40+
+8+%2B+5+=+20x+
+20x+=+13+
+x+=+13%2F20+
This is the fraction of the job Sam and John
complete in +4+ days
there is +1+-+13%2F20+=+7%2F20+ of the job left
------------------------
Let +t+ = time in days for Peter and Sam to
do +7%2F20+ of the job
+1%2F8+%2B+1%2F10+=+%28+7%2F20+%29+%2F+t+
+1%2F8+%2B+1%2F10+=+7%2F20t+
Multiply both sides by +40t+
+5t+%2B+4t+=+14+
+9t+=+14+
+t+=+14%2F9+
+t+=+1+%2B+5%2F9+
-----------------
The job gets done in +4+%2B+1+%2B+5%2F9+
5 and 5/9 days
Hope I got it -get a 2nd opinion, too.