SOLUTION: Three bulldozer operators R, S and T can level off an area for a landing strip in 30 hours. R can do twice as much as S, and S can do 5/3 as much as T. How long would it take each

Question 511722: Three bulldozer operators R, S and T can level off an area for a landing strip in 30 hours. R can do twice as much as S, and S can do 5/3 as much as T. How long would it take each to do the work?
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
Problems like these are fraction problems.
R does 1/R of the job per hr.
S does 1/S of the job per hr.
T does 1/T of the job per hr.
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(1/R per hr + 1/S per hr + 1/T per hr) * 30 hr = 1 whole job
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With three unknowns and one equation, which you cannot solve the problem.
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But we're given some relationships.
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R can do twice as much as S:
1/R = 2 * 1/S = 2/S
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S can do 5/3 as much as T:
1/S = (5/3)*(1/T) = 5/(3T)
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This means R can do 10/3 as much as T
1/R = 2/S = 10/(3T)
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(10/3T + 5/3T + 1/T)* 30 = 1
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Multiply by 3T to eliminate fraction
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(10 + 5 + 3)*30 = 3T
(18)*30 = 3T
3T = 540
T = 180
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T can do the job working alone in 180 hr
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1/S = 5/(3T)
cross multiply
3T = 5S
3(180) = 5S
5S = 540
S = 108
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S can do the job in 108 hr
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1/R = 2/S
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1/R = 2/108
cross multiply
2R = 108
R = 54
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R can do the job in 54 hr
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Check so see if they can the whole job in 30 hrs.
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(1/R + 1/S + 1/T) * 30 = 1 ??
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(1/54 + 1/108 + 1/180) * 30 = (10/540 + 5/540 + 3/540) * 30
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(10/540 + 5/540 + 3/540) * 30 = (18/540) * 30
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(18/540) * 30 = 540/540 = 1
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Correct.
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Answer: Working alone:
R can do the whole job in 54 hr,
S can do the whole job in 108 hr, and
T can do the whole job in 180 hr.
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Done.