SOLUTION: It takes 4 hours for 3 members of Jo's crew to paint the walls of a square room with a side length of 12ft and a 10ft ceiling. How long would it take a crew of five to paint the wa

Algebra ->  Rate-of-work-word-problems -> SOLUTION: It takes 4 hours for 3 members of Jo's crew to paint the walls of a square room with a side length of 12ft and a 10ft ceiling. How long would it take a crew of five to paint the wa      Log On


   

Question 1017683: It takes 4 hours for 3 members of Jo's crew to paint the walls of a square room with a side length of 12ft and a 10ft ceiling. How long would it take a crew of five to paint the walls of a square room with a side length of 25ft and a 12ft ceiling? (Assume there are no windows and they paint over doors, etc)
Found 3 solutions by stanbon, MathTherapy, josmiceli:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
It takes 4 hours for 3 members of Jo's crew to paint the walls of a square room with a side length of 12ft and a 10ft ceiling. How long would it take a crew of five to paint the walls of a square room with a side length of 25ft and a 12ft ceiling? (Assume there are no windows and they paint over doors, etc)
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time is directly related to area and inversely related to crew size
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t = k*a/c
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Solve for "k" using "It takes 4 hours for 3 members of Jo's crew to paint the walls of a square room with a side length of 12ft and a 10ft ceiling"
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4 = k*(4*12*10)/3
k = 1/40
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Equation:
t = a/(40c)
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How long would it take a crew of five to paint the walls of a square room with a side length of 25ft and a 12ft ceiling?
t = (4*23*12)/(40*5)
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time = 5.52 hrs = 5hrs 31min 12sec
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Cheers,
Stan H.

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!
It takes 4 hours for 3 members of Jo's crew to paint the walls of a square room with a side length of 12ft and a 10ft ceiling. How long would it take a crew of five to paint the walls of a square room with a side length of 25ft and a 12ft ceiling? (Assume there are no windows and they paint over doors, etc)
Per-crew-member rate: 1%2F40

Time taken by crew of 3 to paint: matrix%281%2C3%2C480%2Csq%2Cft%29 is: 4 hours

Time taken by crew of 5 to paint: matrix%281%2C3%2C%221%2C200%22%2Csq%2Cft%29 is: highlight_green%286%29 hours

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Find the ratio of the areas of the 2 rooms
1st room:
+A%5B1%5D+=+4%2A12%2A10+
+A%5B1%5D+=+480+ ft2
2nd room:
+A%5B2%5D+=+4%2A25%2A12+
+A%5B2%5D+=+1200+
+A%5B2%5D+%2F+A%5B1%5D+=+2.5%2F1+
+A%5B2%5D+%2F+A%5B1%5D+=+5%2F2+
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Each member of Jo's crew works
at the rate +2%2Ft%5B1%5D+ where +2+
is from the above ratio, and +t+
is time in hrs to do the work
[ 3 members ] / [ 4 hrs ] = [ 2 units of work ] / [ t[1] hrs ]
+3%2F4+=+2%2Ft%5B1%5D+
+3t%5B1%5D+=+8+
+t%5B1%5D+=+8%2F3+ hrs
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For the crew of 5:
[ 5 members ] / [ time for them to finish ] = [ units of work ] / [ time for 1 member ]
+5%2Ft%5B2%5D+=+5%2F%28+8%2F3%29+
+1%2Ft%5B2%5D+=+1%2F%288%2F3%29+
+t%5B2%5D+=+8%2F3+
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I get each crew takes the same time to paint their rooms:
+8%2F3+=+2+%2B+2%2F3+
2 hrs 40 min
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Hope I got it! Definitely get another opinion
on this -my logic could have gotten twisted.