word problem

[neha shekhawat]

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

Hi,
I got confused while solving this question.I can easily solve it by forming equations in terms of rate.But I tried to solve it by using equations in terms of time i.e let rate of maria= M and rate of perry = P
then
1/M + 1/P=45 equation (1)
and another equation 1/M + 1/2M=20 equation (2) by solving this I got 1/M=40/3
using this inserting value of 1/M in equation (1)
I got 1/P=95/3 which is totally different from answer that I got using equations in terms of rate.
Where am I going wrong?
why can't we solve this question using equations in terms of time.
please help

[GMATGuruNY]

Hi,
I got confused while solving this question.I can easily solve it by forming equations in terms of rate.But I tried to solve it by using equations in terms of time i.e let rate of maria= M and rate of perry = P
then
1/M + 1/P=45 equation (1)
and another equation 1/M + 1/2M=20 equation (2) by solving this I got 1/M=40/3
using this inserting value of 1/M in equation (1)
I got 1/P=95/3 which is totally different from answer that I got using equations in terms of rate.
Where am I going wrong?
why can't we solve this question using equations in terms of time.
please help

The equation in red is not valid.
Rates are additive.
Times are not.

Let:
The job = 30 widgets.
M's time = 10 hours.
P's time = 15 hours.
Since M takes 10 hours to produce 30 widgets, M's rate = w/t = 30/10 = 3 widgets per hour.
Since P takes 15 hours to produce 30 widgets, P's rate = w/t = 30/15 = 2 widgets per hour.
Thus, their combined rate = 3+2 = 5 widgets per hour.
Since their combined rate = 5 widgets per hour, the time for M and P together to produce 30 widgets = w/r = 30/5 = 6 hours.

The resulting time for M and P together (6 hours) is MUCH LESS than the sum of their individual times (10+15 = 25).

[Brent@GMATPrepNow]

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 is to assign a 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
output/time = rate
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.
output/time = rate
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

Cheers,
Brent

[[email protected]]

Hi neha shekhawat,

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: E

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

[Jay@ManhattanReview]

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

Hi,
I got confused while solving this question.I can easily solve it by forming equations in terms of rate.But I tried to solve it by using equations in terms of time i.e let rate of maria= M and rate of perry = P
then
1/M + 1/P=45 equation (1)
and another equation 1/M + 1/2M=20 equation (2) by solving this I got 1/M=40/3
using this inserting value of 1/M in equation (1)
I got 1/P=95/3 which is totally different from answer that I got using equations in terms of rate.
Where am I going wrong?
why can't we solve this question using equations in terms of time.
please help

Your Algebra is all fine, but the formation of equations 1/M + 1/P=45 and 1/M + 1/2M=20 is incorrect.

Let M = Time Maria takes to complete the job and P = Time Perry takes to complete the job

Thus, 1/M + 1/P=1/45 and 1/M + 1/P'=1/20; here, P' = Perry's new time = M/2

=> 1/M + 1/(M/2)=1/20 => 1/M + 2/M=1/20

We get 1/M = 1/60.

Plugging in 1/M = 1/60 in 1/M + 1/P=1/45, we get 1/P=1/45 - 1/60 = 1/180.

Or, Perry takes 180' or 3 hrs.

The correct answer: E

Hope this helps!

Get free ebook: Manhattan Review GMAT Quantitative Question Bank

-Jay
_________________
Manhattan Review GMAT Prep

Locations: New York | Frankfurt | Hong Kong | Zurich | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

[Matt@VeritasPrep]

Let's think in terms of rate and time to see what's going on. Since we've got one job to do, we'll say

Work = Rate * Time
1 = (m + p) * t
1/(m + p) = t

Notice how this is slightly different from your first rate? Since they're working together, their joint rate is 1/(m + p), NOT 1/m + 1/p.

Now we've got

1/(m + p) = 45

and

1/(m + 2m) = 20

which gives us p = 1/180. This is Perry's rate, so his time is 180 minutes, or 3 hours.

I wouldn't recommend doing it this way, though: the interpretation of the numbers is counterintuitive.

[Matt@VeritasPrep]

why can't we solve this question using equations in terms of time.

Whoops! I forgot to address this part. We definitely can, as I showed above ... we just might not want to. The rate approach is less prone to error: it's easier to set up and the results make more immediate sense.