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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\(rate*time=work\)

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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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

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??

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
Cheers!
J

1/P + 1/M = 1/45

2/M + 1/M = 1/20

3/M = 1/20 => M=60

1/P + 1/60 = 1/45

P=180 mins, =3 hours

maria's rate=m
if 3m=1/20, then m=1/60
1/45-1/60=1/180=perry's rate
perry needs 180 minutes=3 hours to complete job alone

M's time to complete the job alone = M => time taken to complete 1 unit of work = 1/M
P's time to complete the job alone = P => time taken to complete 1 unit of work = 1/P

Second case, P's rate = 2(M's rate) => to complete the job alone = M/2 => time taken to complete 1 unit of work = 2/M
Now, 1/M + 2/M = 1/20 => M=60mins

First case, 1/M + 1/P = 45
=> 1/60 + 1/P = 1/45
=> P = 180mins = 3hrs

3m*20=(r+m)*45=1(work)
60m=45r+45m
15m=45p
m=3p(substitute in above eq)

3m*20
3(3p)*20
9p*20
p*180
p takes 180 minutes to complete the work at its normal speed
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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:

GMAT assassins aren't born, they're made,
Rich
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