SOLUTION: A contractor hires two bulldozers to clear the trees from a 20 acre tract of land. One works twice as fast as the other. It takes them 3 days to clear the tract working together. H

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Question 1153780: A contractor hires two bulldozers to clear the trees from a 20 acre tract of land. One works twice as fast as the other. It takes them 3 days to clear the tract working together. How long would it take each of them alone?
Found 2 solutions by josmiceli, greenestamps:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Call the clearing of 20 acres 1 job
Let +t+ = time in days for the faster worker to
do the job working alone
+2t+ = time in days for the slower worker to do
the job working alone
------------------------------------------
[ 1 job ] / [ 3 days ] = their rate of woking together
Add their rates working alone to get their rate working together
+1%2Ft+%2B+1%2F%282t%29+=+1%2F3+
Multiply both sides by +6t+
+6+%2B+3+=+2t+
+2t+=+9+
+t+=+4.5+
and
+2t+=+9+
--------------------
The faster worker takes 4.5 days working alone
The slower worker takes 9 days working alone
--------------------
check:
+1%2Ft+%2B+1%2F%282t%29+=+1%2F3+
+1%2F4.5+%2B+1%2F9+=+1%2F3+
Multiply both sides by +9+
+2+%2B+1+=+3+
OK

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


A very different way of solving the problem, which I find much easier and faster....

Since one of the bulldozers works twice as fast as the other, when working together one bulldozer does 2/3 of the work and the other does 1/3.

So the slower bulldozer does 1/3 of the job in 3 days, which means it will take it 9 days to do the job alone.

And the faster bulldozer works twice as fast, so it will take it half as long as the other to do the job alone -- 4.5 days.

ANSWERS:
4.5 days alone for the faster bulldozer
9 days alone for the slower