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30 Dec 2007, 02:50
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3 employers rake the beach each day. working together, employees A and B can rake the beach in 3 hours, whereas A and C can rake the beach in 2.5 h. working together, can A,B, and C rake the beach in less than 2 h?
1. B rakes faster than A
2. working alone, C can rake the beach in less than 5 h
1. B rakes faster than A
2. working alone, C can rake the beach in less than 5 h
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Let a,b,c - rates of A,B, and C.
3*a+3*b=1 ==> a+b=1/3
2.5*a+2.5*c=1 ==> a+c=2/5
t(a+b+c)=1 ==> a+b+c=1/t and t should be less then 2 ==> a+b+c>1/2
1. a+b=1/3 and b>a mean that a<1/6
a+b+c = a+b+a+c-a = 1/3+2/5-a > 1/3+2/5-1/6 = (10+12-5)/30 = 17/30 > 1/2. suff.
2. c>1/5.
a+b+c = 1/3+c > 1/3+1/5 = (3+5)/15 = 8/15 > 1/2. suff.
Let a,b,c - rates of A,B, and C.
3*a+3*b=1 ==> a+b=1/3
2.5*a+2.5*c=1 ==> a+c=2/5
t(a+b+c)=1 ==> a+b+c=1/t and t should be less then 2 ==> a+b+c>1/2
1. a+b=1/3 and b>a mean that a<1/6
a+b+c = a+b+a+c-a = 1/3+2/5-a > 1/3+2/5-1/6 = (10+12-5)/30 = 17/30 > 1/2. suff.
2. c>1/5.
a+b+c = 1/3+c > 1/3+1/5 = (3+5)/15 = 8/15 > 1/2. suff.
30 Dec 2007, 05:00
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walker...can the formula ABC/AB+AC+BC be applied in this case?
