SOLUTION: If joe can wash one car in four hours and Sam can wash one in six hours, how long would it take them to wash twenty cars? The answer I am told is 48, but I think that it is 100,

Algebra ->  Rate-of-work-word-problems -> SOLUTION: If joe can wash one car in four hours and Sam can wash one in six hours, how long would it take them to wash twenty cars? The answer I am told is 48, but I think that it is 100,      Log On


   

Question 1026600: If joe can wash one car in four hours and Sam can wash one in six hours, how long would it take them to wash twenty cars?
The answer I am told is 48, but I think that it is 100, because if they each wash ten, then jor will take fourty hours and Sam will take sixty.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Find out how long it will take them both
to was 1 car. It will take 20 times longer
to wash 20 cars
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Joe's rate of working:
[ 1 car washed ] / [ 4 hrs ]
Sam's rate of working:
[ 1 car washed ] / [ 6 hrs ]
--------------------------
Let +t+ = time in hrs for them to
wash 1 car working together
------------------------------
Add their rates of working to get their rate working together
+1%2F4+%2B+1%2F6+=+1%2Ft+
Multiply both sides by +12t+
+3t+%2B+2t+=+12+
+5t+=+12+
+t+=+12%2F5+ hrs to wash 1 car working together
Now multiply by +20+ for 20 cars
+20%2A%28+12%2F5+%29+=+48+
Working together, it will take them 48 hrs
to wash 20 cars
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A good rule to remember is that, working together, it
always takes less time than the fastest of the
2 workers