SOLUTION: sam and bill can paint a fence in one hour. Sam can paint three times as fast as Bill in any given amount of time. How many minutes would it take Sam to paint the fence alone?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: sam and bill can paint a fence in one hour. Sam can paint three times as fast as Bill in any given amount of time. How many minutes would it take Sam to paint the fence alone?      Log On


   

Question 965020: sam and bill can paint a fence in one hour. Sam can paint three times as fast as Bill in any given amount of time. How many minutes would it take Sam to paint the fence alone?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Working together, their rate is:
[ 1 fence ] / [ 1 hr ]
---------------------
Let +t+ = time in hrs for Sam
to paint fence
+3t+ = time for Bill to paint fence
( 3 times slower )
---------------------
Add their rates of painting to get
their rate painting together
+1%2Ft+%2B+1%2F%283t%29+=+1%2F1+
Multiply both sides by +3t+
+3+%2B+1+=+3t+
+3t+=+4+
+t+=+4%2F3+
and
+3t+=+3%2A%284%2F3%29+
+3t+=+4+
----------------
+t+=+4%2F3+
+t+=+1+%2B+1%2F3+
Convert +1%2F3+ hr to minutes
+%281%2F3%29%2A60+=+20+
Sam takes 1 hr 20 min to paint fence
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check:
+1%2Ft+%2B+1%2F%283t%29+=+1%2F1+
+1%2F%284%2F3%29+%2B+1%2F%283%2A%284%2F3%29%29+=+1%2F1+
+3%2F4+%2B+1%2F4++=+1+
+1+=+1+
OK