SOLUTION: Suppose you hire three 3 toed sloths to build a treehouse. Normally the 3 toed sloths work individually, the first sloth takes 24 hours but only charges 5 dollars an hour, the seco

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Suppose you hire three 3 toed sloths to build a treehouse. Normally the 3 toed sloths work individually, the first sloth takes 24 hours but only charges 5 dollars an hour, the seco      Log On


   

Question 955342: Suppose you hire three 3 toed sloths to build a treehouse. Normally the 3 toed sloths work individually, the first sloth takes 24 hours but only charges 5 dollars an hour, the second sloth takes 16 hours and charges 10 dollars, the third sloth takes 12 hours at 15 dollars an hour. If the three sloths work together, and they start at noon. What time will they be done with the treehouse and how much will it cost?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Working together, they will all work
the same amount of time
Let their time working together = +t+
-----------------------
Add their rates of working to get
rate working together
+1%2F24+%2B+1%2F16+%2B+1%2F12+=+1%2Ft+
Multiply both sides by +48t+
+2t+%2B+3t+%2B+4t+=+48+
+9t+=+48+
+t+=+5.333+
+.333%2A60+=+20+
noon + 5 hrs + 20 min = 5:20 PM
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1st sloth charges:
+5%2A5.333+=+26.667+
2nd sloth charges:
+10%2A5.333+=+53.333+
3rd sloth charges:
+15%2A5.333+=+80+
-------------------
Total charge = +26.667+%2B+53.333+%2B+80+
Total charge = +160+
$160.00