SOLUTION: Fred can mow a lawn in 120 minutes. Rocky can mow the same lawn in 80 minutes. How long does it take for both Fred and Rocky to mow the lawn if they are working together?

Algebra ->  Test -> SOLUTION: Fred can mow a lawn in 120 minutes. Rocky can mow the same lawn in 80 minutes. How long does it take for both Fred and Rocky to mow the lawn if they are working together?      Log On


   

Question 1018913: Fred can mow a lawn in 120 minutes. Rocky can mow the same lawn in 80 minutes. How long does it take for both Fred and Rocky to mow the lawn if they are working together?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = their time in minutes working together
Add their rates of working to get their rate working together
Fred's rate:
[ 1 lawn ] / [ 120 min ]
Rocky's rate:
[ 1 lawn ] / [ 80 min ]
Rate working together:
[ 1 lawn ] / [ t min ]
--------------------
+1%2F120+%2B+1%2F80+=+1%2Ft+
Multiply both sides by +240t+
+2t+%2B+3t+=+240+
+5t+=+240+
+t+=+48+
-------------
It takes them 48 min to mow
lawn working together
--------------------
check:
+1%2F120+%2B+1%2F80+=+1%2Ft+
+1%2F120+%2B+1%2F80+=+1%2F48+
+1%2F30+%2B+1%2F20+=+1%2F12+
+1%2F15+%2B+1%2F10+=+1%2F6+
+.0667+%2B+.1+=+.1667+
+.1667+=+.1667+
OK