SOLUTION: Working alone, Ryan can dig a 10ft by 10ft hole in 5 hours. Castle can dig the same hole in six hours. How long word it take them if they worked together?

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Question 966399: Working alone, Ryan can dig a 10ft by 10ft hole in 5 hours. Castle can dig the same hole in six hours. How long word it take them if they worked together?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Add their rates of working:
Ryan's rate:
[ 1 hole dug ] / [ 5 hrs ]
Castle's rate:
[ 1 hole dug ] / [ 6 hrs ]
------------------------
Let +t+ = their time in hrs working together
+1%2F5+%2B+1%2F6+=+1%2Ft+
Multiply both sides by +30t+
+6t+%2B+5t+=+30+
+11t+=+30+
+t+=+2.727+
+.727%2A60+=+44+
It will take them 2 hrs 44 min working together
-------------------
check:
+1%2F5+%2B+1%2F6+=+1%2Ft+
+1%2F5+%2B+1%2F6+=+1%2F2.727+
+.2+%2B+.1667+=+.3667+
+.3667+=+.3667+
OK