Bunuel wrote:
Painters X and Y are simultaneously painting a house. If together they can paint the house in 25 hours, how many more hours would it take painter X to paint the house if he worked alone?
(1) Painter X's rate is 4/5 that of painter Y.
(2) Painter Y could paint the house alone in 45 hours.
ASIDE: For work questions, there are two useful rules:
Rule #1: If a person can complete an entire job in k hours, then in one hour, the person can complete 1/k of the jobExample: If it takes Sue 5 hours to complete a job, then in one hour, she can complete 1/5 of the job. In other words, her work rate is 1/5 of the job per hour
Rule #2: If a person completes a/b of the job in one hour, then it will take b/a hours to complete the entire jobExample: If Sam can complete 1/8 of the job
in one hour, then it will take him 8/1 hours to complete the job.
Likewise, if Joe can complete 2/3 of the job in one hour, then it will take him 3/2 hours to complete the job.
Let’s use these rules to solve the question. . . .
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Target question: How many hours would it take painter X to paint the house if he worked alone?Aside: If we can determine Painter X's rate, we can answer the target question
Given: Together, painters X and Y can paint the house in 25 hours This means that, in ONE HOUR, they can paint 1/25 of the house
In other words, their combined RATE =
1/25 of the house per hour Statement 1: Painter X's rate is 4/5 that of painter Y So, if we let R = painter Y's HOURLY RATE, we can say that (4/5)R = painter X's HOURLY RATE
Since their combined RATE =
1/25 of the house per hour, we can write: R + (4/5)R =
1/25Since we COULD solve this equation for R, we COULD determine painter X's rate, which means we COULD determine
how long it would take painter X to paint the house alone.
Since we COULD answer the
target question with certainty, statement 1 is SUFFICIENT
Aside: We'd never actually waste our time answering the target question, since we need only determine whether we have sufficient information to answer the target question Statement 2: Painter Y could paint the house alone in 45 hours This means that painter Y's HOURLY RATE =
1/45 of a house PER HOUR
It's given that (painter X's HOURLY RATE) + (painter Y's HOURLY RATE) =
1/25 So, we can now write: (painter X's HOURLY RATE) + (
1/45) =
1/25 Since we COULD use this equation to determine painter X's rate, we COULD determine
how long it would take painter X to paint the house alone.
Since we COULD answer the
target question with certainty, statement 2 is SUFFICIENT
Answer:
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