Two musicians, Maria and Perry, work at independent constant rates to tune a warehouse full of instruments. If both musicians start at the same time and work at their normal rates, they will complete the job in 45 minutes. However, if Perry were to work at twice Maria's rate, they would take only 20 minutes. How long would it take Perry, working alone at his normal rate, to tune the warehouse full of instruments?
A)1 hr 20 min
B)1 hr 45 min
C)2 hr
D)2 hr 20 min
E)3 hr
Another approach:
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. . . .
Let M = the FRACTION of the total job that Maria can complete (
working alone) in 1 MINUTE.
Let P = the FRACTION of the total job that Perry can complete (
working alone) in 1 MINUTE
Both musicians working TOGETHER complete the job in 45 minutes
By Rule #1, we can conclude that, working together, Maria and Perry can complete
1/45 of the total job in 1 MINUTE
So, in 1 MINUTE, we can says that (Maria's contribution) + (Perry's contribution) =
1/45 of the total job
We can write: M + P =
1/45
If Perry were to work at twice Maria's rate, they would take only 20 minutes.
By Rule #1, we can conclude that, working together, Maria and Perry can complete
1/20 of the total job in 1 MINUTE
So, in 1 MINUTE, we can says that (Maria's contribution) + (Perry's contribution) =
1/20 of the total job
If Perry's rate is twice Maria's, then in 1 MINUTE, the fraction of the job that Perry can complete = 2M
So, we can write: M + 2M =
1/20
Simplify: 3M = 1/20
Solve: M =
1/60 (In 1 MINUTE, Maria can complete 1/60 of the job)
Now that we've solved for M, we can take the equation M + P =
1/45 and replace M with
1/60 to get:
1/60 + P =
1/45
Rewrite using common denominator: 3/180 + P = 4/180
Solve: P = 1/80
So, in 1 MINUTE, Perry can complete 1/180 of the job
By Rule #2, we can conclude that Perry can complete the ENTIRE job in
180 minutes.
Answer:
E
Cheers,
Brent
