SOLUTION: Joe can mow the eighteenth fairway in 4 hours. Bob can do it in 3 hours. Joe, Bob, and Tom working together can do it in an hour and twenty minutes. How long would it take Tom to d

Algebra ->  Customizable Word Problem Solvers  -> Mixtures -> SOLUTION: Joe can mow the eighteenth fairway in 4 hours. Bob can do it in 3 hours. Joe, Bob, and Tom working together can do it in an hour and twenty minutes. How long would it take Tom to d      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


   



Question 1029143: Joe can mow the eighteenth fairway in 4 hours. Bob can do it in 3 hours. Joe, Bob, and Tom working together can do it in an hour and twenty minutes. How long would it take Tom to do the job working alone?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Add their rates of mowing to
get rate mowing together
Joe's rate:
[ 1 job / 8 hrs ]
Bob's rate:
[ 1 job / 3 hrs ]
Let +t+ = Tom's rate for the job
---------------
+1%2F8+%2B+1%2F4+%2B+1%2Ft+=+1%2F%28%28+4%2F3%29%29+
+1%2F8+%2B+1%2F4+%2B+1%2Ft+=+3%2F4+
( +4%2F3+ hrs = 1 hr 20 min )
Multiply both sides by +8t+
+t+%2B+2t+%2B+8+=+6t+
+3t+=+8+
+t+=+2+%2B+2%2F3+
Tom takes 2 hrs 40 min working alone
-------------
check:
+1%2F8+%2B+1%2F4+%2B+1%2Ft+=+3%2F4+
+1%2F8+%2B+1%2F4+%2B+1%2F%28%288%2F3%29%29+=+1%2F%28%284%2F3%29%29+
+.125+%2B+.25+%2B+.375+=+.75+
+.75+=+.75+
OK