SOLUTION: Pam and John, working together, can mow the lawn in 2 hours. Working alone, John takes twice as long as Pam. How long does it take Pam to mow the lawn alone?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Pam and John, working together, can mow the lawn in 2 hours. Working alone, John takes twice as long as Pam. How long does it take Pam to mow the lawn alone?      Log On


   

Question 1157699: Pam and John, working together, can mow the lawn in 2 hours. Working alone, John takes twice as long as Pam. How long does it take Pam to mow the lawn alone?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Their rate working together is
[ 1 job done ] / [ 2 hrs ] = +1%2F2+
Let +t+ = time in hrs for Pam to
mow the lawn alone
Pam's rate is +1%2Ft+
John's rate is +1%2F%282t%29+
------------------------------
Add their rates to get the rate working together
+1%2Ft+%2B+1%2F%282t%29+=+1%2F2+
Multiply both sides by +2t+
+2+%2B+1+=+t+
+t+=+3+ hrs
Pam takes 3 hrs working alone
-------------------------------------
check:
+1%2Ft+%2B+1%2F%282t%29+=+1%2F2+
+1%2F3+%2B+1%2F6+=+1%2F2+
+2%2F6+%2B+1%2F6+=+3%2F6+
OK