BTGmoderatorDC wrote:A paint crew gets a rush order to paint 80 houses in a new development. They paint the first y houses at a rate of x houses per week. Realizing that they'll be late at this rate, they bring in some more painters and paint the rest of the houses at the rate of 1.25x houses per week. The total time it takes them to paint all the houses under this scenario is what fraction of the time it would have taken if they had painted all the houses at their original rate of x houses per week?
(A) 0.8(80 - y)
(B) 0.8 + 0.0025y
(C) 80/y - 1.25
(D) 80/1.25y
(E) 80 - 0.25y
Let y=0, implying that NONE of the 80 houses are painted at the original rate of x houses per week, with the result that ALL 80 houses are painted at the greater rate of (5/4)x houses per week.
The total time it takes them to paint all the houses under this scenario is what fraction of the time it would have taken if they had painted all the houses at their original rate?
Time and rate have a RECIPROCAL RELATIONSHIP.
Since the rate for painting all 80 houses is 5/4 the original rate, the time for painting all 80 houses is 4/5 of the original time.
The correct answer must yield 4/5 when y=0.
Only B works:
0.8 + 0.0025y = 0.8 = 4/5.
The correct answer is
B.
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