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
D2 hr 20 min
E 3 hr
E
What's the simplest way of attacking these type of problems?
Musicians at work
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Assume the total work to b 180 .. given time taken by perry and maria is 45minutes .. i.e rate =180/45 = 4 per minute by both.
now if perry to work twice maria's rate ,it will take 20min i.e 2maria+maria=20mins i.e 3maria=180/20
gives maria rate as 3 per min,that means perrys rate is 1 per minute as 4 per minute is the total rate of perry and maria
perry's rate 180/1 = 3 hours
now if perry to work twice maria's rate ,it will take 20min i.e 2maria+maria=20mins i.e 3maria=180/20
gives maria rate as 3 per min,that means perrys rate is 1 per minute as 4 per minute is the total rate of perry and maria
perry's rate 180/1 = 3 hours
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Let us assume they can tune m and p instruments per minute, respectively, if they work separately.
So, together in 1 minute they can tune (m + p) instruments.
So, together in 45 minutes they can tune 45(m + p) instruments.
So, there are a total of 45(m + p) instruments in the warehouse.
Now, if Perry were to work at twice Maria's rate, i.e. Perry could tune 2m instruments per minute, together in one minute they will tune (2m + m) = 3m instruments.
So, together in 20 minutes they can tune 20*(3m) = 60m instruments.
So, 45(m + p) = 60m
So, 45p = 15m
So, p = m/3
Now, there are 60m instruments and Perry can tune m/3 instruments per minute.
So, Perry alone will take 60m/(m/3) minutes = 180 minutes = 3 hours to tune the warehouse full of instruments.
Answer : E
So, together in 1 minute they can tune (m + p) instruments.
So, together in 45 minutes they can tune 45(m + p) instruments.
So, there are a total of 45(m + p) instruments in the warehouse.
Now, if Perry were to work at twice Maria's rate, i.e. Perry could tune 2m instruments per minute, together in one minute they will tune (2m + m) = 3m instruments.
So, together in 20 minutes they can tune 20*(3m) = 60m instruments.
So, 45(m + p) = 60m
So, 45p = 15m
So, p = m/3
Now, there are 60m instruments and Perry can tune m/3 instruments per minute.
So, Perry alone will take 60m/(m/3) minutes = 180 minutes = 3 hours to tune the warehouse full of instruments.
Answer : E
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Time they take in inversely proportional to their efficiencies. You can add/subtract efficiencies when they work together.serendipiteez wrote: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
D2 hr 20 min
E 3 hr
E
What's the simplest way of attacking these type of problems?
P+M = 1/45
If P=2M
3M=1/20
M=1/60
p=1/45-1/60 = 1/180
So, 3 hrs
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Let the job = the LCM of 45 and 20 = 180 units.serendipiteez wrote: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
D2 hr 20 min
E 3 hr
Since Maria and Perry working at their normal rates take 45 minutes, the combined normal rate for M+P = w/t = 180/45 = 4 units per minute.
When Perry works at twice Maria's rate, the combined faster rate for P+M = 2M + M = 3M.
Since the time decreases to 20 minutes, the rate for 3M = w/t = 180/20 = 9 units per minute.
Since the rate for 3M = 9 units per minute, the rate for M alone = 3 units per minute.
P's rate alone = combined normal rate for P+M - M's rate = 4-3 = 1 unit per minute.
Thus:
Time for P alone = w/r = 180/1 = 180 minutes = 3 hours.
The correct answer is E.
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For me the best way to approach this question and any work problem is using the combined work formula: A*B/A+Bserendipiteez wrote: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
D2 hr 20 min
E 3 hr
E
What's the simplest way of attacking these type of problems?
But you always have to pay attention to 2 things:
- The formula is about A and B TIME to complete a job
- The TIME to complete a job is inversely proportional to the RATE
So the calcutation would be:
M = Maria time to complete
P = Perry time to complete
M*P/M+P = 45 minutes
When Perry works at TWICE Maria's rate, he will take HALF of Maria's time to complete (The new P will be M/2, NOT 2M!!! Remember the formula is about time, no need to deal with confusing Rates and # of instruments)
(M*M/2)/M+(M/2)= 20 minutes => M = 60 minutes
Now just plug the M to find P:
60*P/(60+P) = 45 minutes => P = 180 minutes = 3 hours
You can also convert the minutes into hours and it will be super easy to calculate:
- 20 minutes = 1/3 hour
- 45 minutes = 3/4 hour
Hope that can help you and the readers!
niddy
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Another approach:serendipiteez wrote: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
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
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Brent
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We can let the time it takes Perry to complete the job alone = p and the time it takes Maria to complete the job alone = m. Thus, Perry's rate = 1/p and Maria's rate = 1/m. Since they complete the job in 45 minutes, we use the formula work = rate x time to get:serendipiteez wrote: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
D2 hr 20 min
E 3 hr
(1/m)45 + (1/p)45 = 1
45/m + 45/p = 1
Multiplying the entire equation by mp, we have:
45p + 45m = mp
We are also given that if Perry were to work at twice Maria's rate, they would take only 20 minutes. Since Maria's rate is 1/m, Perry's rate would be 2/m. We can create the following equation to determine p:
(2/m)20 + (1/m)20 = 1
40/m + 20/m = 1
Multiplying the entire equation by m, we have:
40 + 20 = m
m = 60
Recalling that 45p + 45m = mp, we can substitute m = 60 in the equation and solve for p:
45p + 45(60) = 60p
3p + 3(60) = 4p
180 = p
Since Perry's time is 180 minutes, and 60 minutes = 1 hour, it takes him 3 hours to complete the job at his normal rate.
Answer: E
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