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

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)   (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)   (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:
Time taken by crew of 3 to paint: is: 4 hours
Time taken by crew of 5 to paint: is: hours
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
Find the ratio of the areas of the 2 rooms
1st room:

ft2
2nd room:

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Each member of Jo's crew works
at the rate where
is from the above ratio, and
is time in hrs to do the work
[ 3 members ] / [ 4 hrs ] = [ 2 units of work ] / [ t[1] hrs ]

hrs
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For the crew of 5:
[ 5 members ] / [ time for them to finish ] = [ units of work ] / [ time for 1 member ]

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I get each crew takes the same time to paint their rooms:

2 hrs 40 min
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Hope I got it! Definitely get another opinion
on this -my logic could have gotten twisted.
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