SOLUTION: It takes 3 hours to 4 adults to build a sand castle. It takes 4 hours to 6 children to build the same sand castle. How many hours will it take to 6 adults and 3 children to build a

Algebra ->  Equations -> SOLUTION: It takes 3 hours to 4 adults to build a sand castle. It takes 4 hours to 6 children to build the same sand castle. How many hours will it take to 6 adults and 3 children to build a      Log On


   

Question 1006273: It takes 3 hours to 4 adults to build a sand castle. It takes 4 hours to 6 children to build the same sand castle. How many hours will it take to 6 adults and 3 children to build a castle?
(I don't know where to start! - thank you)
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
1 adult will take 4 times as long to
build 1 sand castle, so
-----------------------
1 adult takes 12 hours to build 1 sand castle
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1 child will take 6 times as long
to build 1 sand castle, so
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1 child takes 24 hours to build 1 sand castle
-----------------------
The rate of building for adults is:
[ 1 sand castle ] / [ 12 hr ]
-----------------------
The rate of building for children is:
[ 1 sand castle ] / [ 24 hr ]
-----------------------
Multiply these rates times people doing the work
and add the rates to get rate working together
Let +1%2Ft+ = the rate of:
[ 1 sand castle ] / [ t hrs ]
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+6%2A%28+1%2F12+%29+%2B+3%2A%28+1%2F24+%29+=+1%2Ft+
Multiply both sides by +24t+
+12t+%2B+3t+=+24+
+15t+=+24+
+t+=+1.6+
+.6%2A60+=+36+
6 adults and 3 children can build 1 sand castle
in 1 hr 36 min
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Hope I got it -a 2nd opinion wouldn't hurt either