gmatdriller wrote:A qualified worker digs a well in 5 hours. He invites 2 apprentices, both capable of working 3/4 as fast and 2 trainees both working 1/5 as fast as he. If the five-person team digs the same well, how much time does the team need to finish the job?
A. 1:24
B. 1:34
C. 1:44
D. 1:54
E. 2:14
I prefer the approach Mitch used, however here's another solution:
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 job
Example: 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 job
Example: 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. . . .
A qualified worker digs a well in 5 hours
Applying Rule #1, we know that in
ONE HOUR, the worker can complete
1/5 of the job.
ASIDE: This means the worker's
rate =
1/5 of the job per hour.
Each apprentice works 3/4 as fast
So, in
ONE HOUR, an apprentice can complete (
3/4)
(1/5) of the job.
In other words, each apprentice can complete
3/20 of the job in 1 hour.
Each trainee works 1/5 as fast
So, in
ONE HOUR, a trainee can complete (
1/5)
(1/5) of the job.
In other words, each trainee can complete
1/25 of the job in 1 hour.
So, in ONE HOUR, the
total work completed =
1/5 +
3/20 +
3/20 +
1/25 +
1/25
Add fractions with common denominator of 100 to get:
20/100 +
15/100 +
15/100 +
4/100 +
4/100
Combine to get: 58/100
In other words, in ONE HOUR, the team can complete 58/100 of the job.
Applying Rule #2, the time to complete the entire job = 100/58 hours.
100/58 = 1 42/58
IMPORTANT: 42/60 = 42 minutes. So, 42/58 will be a little bit MORE than 42 minutes.
Answer choice [spoiler] C (with 44 minutes)[/spoiler] is the best option.
Answer:
C
Cheers,
Brent
