A paint crew gets a rush order to paint 80 houses in a new development

Question

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

(A) 0.8(80 – y) 
(B) 0.8 + 0.0025y 
(C) 80/y – 1.25 
(D) 80/1.25y 
(E) 80 – 0.25y

Bunuel · Answer

Re-worded MGMAT question: https://gmatclub.com/forum/a-painting-c ... 99562.html

gmatcafe · Answer

If worked at the original rate it takes 80/x weeks
If worked under new scenario it takes y/x + (80 - y)/1.25x = (1.25y + 80 - y) / 1.25x = (0.25y + 80)/1.25x 
((0.25y + 80)/1.25x) / (80/x) = 0.0025y + 0.8 B)

TheVDR · Answer

Question asks "what fraction" ?
If all houses were done at the same rate, i.e., x houses per week, then the fraction of new time to old time would be 1 (as we haven't changed our rate of work)

Thus, y = 80 should yield 1 as answer.

A, C, D and E gets eliminated straight away.

B gives 1 at y = 80.
Answer (B)

A paint crew gets a rush order to paint 80 houses in a new development

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