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Two musicians, Maria and Perry, work at independent constant 08 Jun 2013, 08:13
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73% (02:37) correct 27% (02:59) wrong based on 1938 sessions

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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
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E
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Two musicians, Maria and Perry, work at independent constant 08 Jun 2013, 08:22
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\(rate*time=work\)

Working together :
\((P+M)*\frac{3}{4}=1\)
If P=2M:
\((2M+M)*\frac{1}{3}=1\) from this we get \(M=1\).

We plug M=1 in the above equation:

\(\frac{3}{4}P+\frac{3}{4}=1\) or \(\frac{3}{4}P=\frac{1}{4}\) \(P=\frac{1}{3}\).

So it would take 3 hours to complete the job, \(\frac{1}{3}*3h=1job\)
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Two musicians, Maria and Perry, work at independent constant 21 Jan 2014, 03:02
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rawjetraw
Hi Bunuel,

I cant seem to understand what I am doing wrong by solving it like this.. please guide me ..

given: let call maria =m perry = p
working together we have \(\frac{1}{m} + \frac{1}{p} = \frac{1}{45}\) ----------eq 1.

now if perry works twice at maria's rate we get .... \(\frac{1}{m} + \frac{1}{2m} = \frac{1}{20}\)
solving this we get... M = 30

now substituting it in the first eq 1.
\(\frac{1}{30} + \frac{1}{p} = \frac{1}{45}\)

obviously since I am solving inccorectly i get a negative value .. I understand the simple methods give in the above discussions .. i get it .. but what em i doing wrong.. i need to rectify my thought process otherwise I will keep approaching such problems in a similar fashion even in the future..

so comment will be greatly appreciated Bunuel .. Thanks a ton! :idea:
Show more

In your solution m and p are individual times, while 1/m and 1/p are respective rates. If Perry were to work at twice Maria’s rate, then his rate would be 2*(1/m), not 1/(2m). Therefore the correct equations are 1/m+1/p=1/45 and 1/m+2/m=1/20
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Two musicians, Maria and Perry, work at independent constant 08 Jun 2013, 08:30
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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
Show more

Let the whole work be 180 units.

In this case combined rate of Maria and Perry is 180/45=4 units per minute --> M+P=4, where M and P are individual rates of Maria and Perry.

If Perry were to work at twice Maria’s rate, they would take only 20 minutes --> in this case combined rate of Maria and Perry is 180/20=9 units per minute --> M+2M=9 --> M=3 units per minute.

M+P=4 --> 3+P=4 --> P=1 unit per minute.

Time to do 180 units = (job)/(rate) = 180/1 =180 minutes = 3 hours.

Answer: E.
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Two musicians, Maria and Perry, work at independent constant 08 Sep 2013, 12:09
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Rock750
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
Show more


Sol:

Lets Perry Rate be P and Rate of Maria be M
(rate)*(time)= Work or rate = work/time

first equation=> P+M = 1/45
converting it to hrs P+M= 1/(45/60) => 1/(3/4) =>4/3

second equation => M+2M =>1/20
converting it to hrs 3M=1/(20/60) =>1/(1/3) =>3

therefore M= 1 and P=1/3

Rate of Perry = 1/3
time= work/rate (work = 1 job)
Time= 3 hrs
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Two musicians, Maria and Perry, work at independent constant 21 Jan 2014, 00:48
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Hi Bunuel,

I cant seem to understand what I am doing wrong by solving it like this.. please guide me ..

given: let call maria =m perry = p
working together we have \(\frac{1}{m} + \frac{1}{p} = \frac{1}{45}\) ----------eq 1.

now if perry works twice at maria's rate we get .... \(\frac{1}{m} + \frac{1}{2m} = \frac{1}{20}\)
solving this we get... M = 30

now substituting it in the first eq 1.
\(\frac{1}{30} + \frac{1}{p} = \frac{1}{45}\)

obviously since I am solving inccorectly i get a negative value .. I understand the simple methods give in the above discussions .. i get it .. but what em i doing wrong.. i need to rectify my thought process otherwise I will keep approaching such problems in a similar fashion even in the future..

so comment will be greatly appreciated Bunuel .. Thanks a ton! :idea:
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Two musicians, Maria and Perry, work at independent constant 04 Feb 2014, 04:49
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rawjetraw
Hi Bunuel,

I cant seem to understand what I am doing wrong by solving it like this.. please guide me ..

given: let call maria =m perry = p
working together we have \(\frac{1}{m} + \frac{1}{p} = \frac{1}{45}\) ----------eq 1.

now if perry works twice at maria's rate we get .... \(\frac{1}{m} + \frac{1}{2m} = \frac{1}{20}\)
solving this we get... M = 30

now substituting it in the first eq 1.
\(\frac{1}{30} + \frac{1}{p} = \frac{1}{45}\)

obviously since I am solving inccorectly i get a negative value .. I understand the simple methods give in the above discussions .. i get it .. but what em i doing wrong.. i need to rectify my thought process otherwise I will keep approaching such problems in a similar fashion even in the future..

so comment will be greatly appreciated Bunuel .. Thanks a ton! :idea:

In your solution m and p are individual times, while 1/m and 1/p are respective rates. If Perry were to work at twice Maria’s rate, then his rate would be 2*(1/m), not 1/(2m). Therefore the correct equations are 1/m+1/p=1/45 and 1/m+2/m=1/20
Show more

buneul

by the equations 1/m+2/m =1/ 20 => m = 60.

when i substituted in 1/m+1/p = 1/45. i got p = 18.

How to proceed after that??
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Two musicians, Maria and Perry, work at independent constant 04 Feb 2014, 07:15
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Bunuel
rawjetraw
Hi Bunuel,

I cant seem to understand what I am doing wrong by solving it like this.. please guide me ..

given: let call maria =m perry = p
working together we have \(\frac{1}{m} + \frac{1}{p} = \frac{1}{45}\) ----------eq 1.

now if perry works twice at maria's rate we get .... \(\frac{1}{m} + \frac{1}{2m} = \frac{1}{20}\)
solving this we get... M = 30

now substituting it in the first eq 1.
\(\frac{1}{30} + \frac{1}{p} = \frac{1}{45}\)

obviously since I am solving inccorectly i get a negative value .. I understand the simple methods give in the above discussions .. i get it .. but what em i doing wrong.. i need to rectify my thought process otherwise I will keep approaching such problems in a similar fashion even in the future..

so comment will be greatly appreciated Bunuel .. Thanks a ton! :idea:

In your solution m and p are individual times, while 1/m and 1/p are respective rates. If Perry were to work at twice Maria’s rate, then his rate would be 2*(1/m), not 1/(2m). Therefore the correct equations are 1/m+1/p=1/45 and 1/m+2/m=1/20

buneul

by the equations 1/m+2/m =1/ 20 => m = 60.

when i substituted in 1/m+1/p = 1/45. i got p = 18.

How to proceed after that??
Show more

From 1/60 + 1/p = 1/45 it follows that p = 180 minutes, not 18. p there denotes is time Perry needs to compete the job alone, and this is what we need to find, hence p = 180 minutes = 3 hours is the answer.

Hope it's clear.
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Two musicians, Maria and Perry, work at independent constant 14 Apr 2014, 15:05
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So we have the following

1/M + 1/P = 1/45

We also know that 1/M + 2/M = 1/20

Therefore we know that M=60 and by substituting in the first equation we have that 1/P = 1/180

Therefore P = 180 = 3 hours

Hope this clarifies
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Two musicians, Maria and Perry, work at independent constant 29 Apr 2017, 08:56
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Rock750
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
Show more

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:

(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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Two musicians, Maria and Perry, work at independent constant 17 Jan 2018, 13:56
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Hi All,

This question is a complex version of a Work-Formula question, but can still be solved using the Work Formula (you have to be careful to make sure that you're using the formula properly though...

Work = (A)(B)/(A+B) where A and B are the individual rates of the two entities working on their own to complete a task.

Here, we're told that Maria (M) and Perry (P) work on a task together. Working their standard rates, they will complete the job in 45 minutes. We can write this as....

(M)(P)/(M+P) = 45

Next, we're told that IF Perry worked TWICE Maria's rate, then they would take only 20 minutes to complete the task. This means that Perry works TWICE AS FAST as Maria - to write this mathematically, instead of writing P, we have to write (M/2) - since M represents the amount of time that Maria would take to complete the job, M/2 is the equivalent of TWICE Maria's rate...

(M/2)(M)/(M/2 + M) = 20

From here, we have a 'system' - two variables and two unique equations, so we CAN solve for P...

With the second equation, we have...

(M^2)/2 = 10M + 20M
(M^2)/2 = 30M
M^2 = 60M
M = 60

Plugging this value back into the first equation, we have...

MP/(M+P) = 45
60P/(60 + P) = 45
60P = 60(45) + 45P
15P = 60(45)
P = 60(3)
P = 180 minutes

Final Answer:
Show Spoiler
E


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Two musicians, Maria and Perry, work at independent constant 10 Apr 2018, 11:34
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Bunuel chetan2u

Quote:
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
Show more

Let the whole work be 180 units.

Is the highlighted text LCM of 45 and 20? If so, are not these mentioned as time units in main question stem?
How can I use smart numbers for two different variables wiz units and time?
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Two musicians, Maria and Perry, work at independent constant 10 Apr 2018, 21:58
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Bunuel chetan2u

Quote:
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

Let the whole work be 180 units.

Is the highlighted text LCM of 45 and 20? If so, are not these mentioned as time units in main question stem?
How can I use smart numbers for two different variables wiz units and time?
Show more

Hi...

It is taken as LCM of 45 and 20....
You have to just realize that what ever value you take, it will have t o be divided by 45 and 20..

otherwise..
M and P together do in 45 min..
Twice M + M or 3 Ms do in 20 min, so M will do in \(20*3= 60\) min.

So if P joins M, it takes 45 min instead of 60 min..
But for 45 minutes M is also working, so work P does in 45 minutes saves 15 minutes of M work...
This means P takes \(\frac{45}{15}\) times M's time, so \(60*3=180\) min..
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Two musicians, Maria and Perry, work at independent constant 16 Nov 2020, 14:44
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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
Show more

One option is to assign a "nice" value to the total job.
Since the Least Common Multiple of 45 and 20 is 180, let's say that there are 180 instruments in the warehouse.

Let M = the number of instruments that Maria can tune PER MINUTE
Let P = the number of instruments that Perry can tune PER MINUTE

Both musicians working TOGETHER complete the job in 45 minutes
180/45 = 4
So, working TOGETHER, they can tune 4 instruments PER MINUTE
In other words, (Mary's rate) + (Perry's rate) = 4
We can write: M + P = 4

If Perry were to work at twice Maria’s rate, they would take only 20 minutes.
180/20 = 9
So, in this scenario, they can tune 9 instruments PER MINUTE
In other words, (Mary's rate) + (Perry's rate) = 9
In this scenario, Perry's rate = 2M
So, we can write: M + 2M = 9
Simplify: 3M = 9
So, M = 3 (Maria can tune 3 instruments per minute)

Now that we know the value of M, we can use the equation M + P = 4 to conclude that P = 1
In other words, Perry can tune 1 instrument per minute

If there are 180 instruments to tune, it will take Perry 180 minutes to complete the job.

Answer: E
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Two musicians, Maria and Perry, work at independent constant 08 Jan 2022, 04:28
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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
Show more

We can solve the question orally using ratios.

Say Maria's rate is m and Perry's rate is p (only to explain the solution).

When rate is m + p, time taken is 45 mins. (When Maria and Perry work at their own rates)
But when rate is 3m, time taken is 20 mins. (When Maria works at her own rate but Perry works as twice of Maria's rate)

So if rate were m, time taken would be 60 mins. (If rate were 1/3rd, time would become 3 times).

So Maria alone takes 60 mins but Maria and Perry together take 45 mins i.e. the ratio of time taken is 4:3.
Then, ratio of rates is 3:4 which is m : (m+p).
Hence, if m = 3, p = 1.

Hence, rate of Perry alone is 1/3rd the rate of Maria and hence Perry alone will take time which is 3 times the time taken by Maria alone. Since Maria alone takes 60 mins i.e. 1 hr, Perry alone will take 3 hrs.

Answer (E)
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Two musicians, Maria and Perry, work at independent constant 03 Apr 2024, 03:12
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Ans (E)

­Let \(p\) and \(m\) be the time taken by Perry and Maria respectively.

Then their work rates will be: \(\frac{1}{p}\) + \(\frac{1}{m}\) = \(\frac{1}{45}\)  ...(1)

Now, it is given that if Perry works twice of Maria’s rate: \(\frac{1}{p}\) = \(2*\frac{1}{m}\), then it would take only 20 minutes to finish the job.

Therefore, \(\frac{1}{p}\) + \(2*\frac{1}{m}\) = \(\frac{1}{20}\)­

Solving for \(m\), we will get \(m\) = \(60 \ mins\).

Plugging \(m = 60\) in eq. (1):

-> \(\frac{1}{p}\) + \(\frac{1}{60}\) = \(\frac{1}{45}\)

-> \(\frac{1}{p}\) = \(\frac{1}{45}\) \(-\) \(\frac{1}{60}\) = \(\frac{4-3}{180}\) = \(\frac{1}{180}\)

So, \(p\) = \(180 \ mins\) = \(3 \ hours\)­
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Two musicians, Maria and Perry, work at independent constant 23 Aug 2024, 05:21
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Hi Bunuel why did we multiply the rate by 2 and why is 1/2m wrong?
Bunuel

rawjetraw
Hi Bunuel,

I cant seem to understand what I am doing wrong by solving it like this.. please guide me ..

given: let call maria =m perry = p
working together we have \(\frac{1}{m} + \frac{1}{p} = \frac{1}{45}\) ----------eq 1.

now if perry works twice at maria's rate we get .... \(\frac{1}{m} + \frac{1}{2m} = \frac{1}{20}\)
solving this we get... M = 30

now substituting it in the first eq 1.
\(\frac{1}{30} + \frac{1}{p} = \frac{1}{45}\)

obviously since I am solving inccorectly i get a negative value .. I understand the simple methods give in the above discussions .. i get it .. but what em i doing wrong.. i need to rectify my thought process otherwise I will keep approaching such problems in a similar fashion even in the future..

so comment will be greatly appreciated Bunuel .. Thanks a ton! :idea:
In your solution m and p are individual times, while 1/m and 1/p are respective rates. If Perry were to work at twice Maria’s rate, then his rate would be 2*(1/m), not 1/(2m). Therefore the correct equations are 1/m+1/p=1/45 and 1/m+2/m=1/20
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Two musicians, Maria and Perry, work at independent constant 23 Aug 2024, 07:19
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Hi Bunuel why did we multiply the rate by 2 and why is 1/2m wrong?
Bunuel

rawjetraw
Hi Bunuel,

I cant seem to understand what I am doing wrong by solving it like this.. please guide me ..

given: let call maria =m perry = p
working together we have \(\frac{1}{m} + \frac{1}{p} = \frac{1}{45}\) ----------eq 1.

now if perry works twice at maria's rate we get .... \(\frac{1}{m} + \frac{1}{2m} = \frac{1}{20}\)
solving this we get... M = 30

now substituting it in the first eq 1.
\(\frac{1}{30} + \frac{1}{p} = \frac{1}{45}\)

obviously since I am solving inccorectly i get a negative value .. I understand the simple methods give in the above discussions .. i get it .. but what em i doing wrong.. i need to rectify my thought process otherwise I will keep approaching such problems in a similar fashion even in the future..

so comment will be greatly appreciated Bunuel .. Thanks a ton! :idea:
In your solution m and p are individual times, while 1/m and 1/p are respective rates. If Perry were to work at twice Maria’s rate, then his rate would be 2*(1/m), not 1/(2m). Therefore the correct equations are 1/m+1/p=1/45 and 1/m+2/m=1/20
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If m represents the time, in hours, needed for Maria to complete the job, her rate, since the rate is the reciprocal of time, would be 1/time = 1/m work per hour. Twice that rate would be 2 * (1/m) = 2/m.

Hope it helps.
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Two musicians, Maria and Perry, work at independent constant 08 Sep 2025, 18:07
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Let m = Maria's rate of Work
Let p = Perry's rate of Work

The Work achieved in both cases is the same, so we have

45*m + 45*p = 20*2m + 20*m (where 2m represents the new work rate of Perry and m represents the usual work rate of maria)

The above equation simplifies to

45(m+p) = 60m

Therefore; m/(m+p) = 3/4

The above equation means that Maria contributes to 75% of the work when both work together at their normal rates, m & p. This means at Perry's normal rate, she only does 25% of the work.

When they work at their normal rates, the given job takes 45 minutes. Another way of saying this is, Perry does only 25% of the work in 45 minutes. Therefore, for Perry to do 100% of the work she will take 45*4 = 3 hours! Answer is E.
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Two musicians, Maria and Perry, work at independent constant 01 Dec 2025, 11:16
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Maria = M Perry = P

1/M + 1/P =1/(3/4)

1/M + 1/2M = 1/(1/3)

M= 1/2

I then plugged into the original equation

1/(1/2) + 1/P = 1/(3/4)

I got an answer of 1/P = -2/3

I need to know why it's negative. Although I selected 3, something seems off. Bunuel

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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
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