Peter can do a piece of work in 8 days, Sam in 10 days, and Jhohn in 16 days, Sam and John work together can do it in 12 days and then John is replaced by Peter. Find when the work will be finished
Answers
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Peter's rate:
[ 1 job done ] / [ 8 days ]
Sam's rate:
[ 1 job done ] / [ 10 days ]
John's rate:
[ 1 job done ] / [ 16 days ]
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Let +x+ = the fraction of the job that
Sam and John get done in +4+ days
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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
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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.