Two musicians, Maria and Perry, work at independent constant

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

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!

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??

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.

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

Hello Bunuel,
If rates are 1/m & 1/p then pm/(p+m)=45. Now if 1/p=2/m, I substituted m=2p in pm/(p+m)=20, which resulted in p=30... where I am going wrong... Please help.

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

Made same mistake.

if rate p = 2m then time p = m/2. So:

[m/2 * m] / [ m/2 + m] = 20. Calculate and you will get m = 60.

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

first of all. the question is ambiguous from the start. is 45 min the rate they work both together? or each independently?

I suppose together...
so
\(\frac{1}{M}+\frac{1}{P}=\frac{1}{45}\)
then
we are told:
\(\frac{2}{M}+\frac{1}{M}=\frac{1}{20}\)

we can find the rate for M:
\(\frac{1}{60}\) -> so M needs 60 min to finish the job.

now, we are given \(\frac{1}{M}\), we can find \(\frac{1}{P}\)

\(\frac{1}{60}+\frac{1}{P}=\frac{1}{45}\)
\(\frac{1}{P}=\frac{1}{180}\)
So M needs 180 mins, or 3hours to complete the 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

hi
Ofcourse best method would be by rate only but since you want to know a method by time, one such will be

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 45/15 times M's time, so 60*3=180 min..

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

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

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

Bunuel chetan2u



Let the whole work be 180 units.

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