Two musicians, Maria and Perry, work at independent constant rates to tune a warehouse full of instruments. If both

[M7MBA]

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

[spoiler]OA=E[/spoiler]

Source: Manhattan GMAT

[anonylfc]

You might want to do this in the traditional fraction way, however I hate that method. I always take a number which will be easily dividable by the given numbers and then proceed - for such work problems.

How to chose that number? Okay 45 mins and 20 mins are basically 3/4 and 1/3 of an hour. LCM of 4 and 3 is 12. So I will take 120 as the TOTAL WORK TO BE DONE.
We will first solve the second condition,
=> Perry (x) works at twice the rate of Martha (y)
=> x=2y

Now the condition says they can complete the work in 20 mins which is 1/3 of an hour. Hence the equation boils down to
=> 1(x+y)/3=120
But x=2y
=>3y/3=120
=y=120

Now, According to first condition
=> 3(x+y)/4 =120
=>3x+3y=480
From previous condition y=120
=>3x+3(120)=480
=> 3x = 480-360
=>3x = 120
=> x=40

Which is the answer. Hope this was helpful.

[Scott@TargetTestPrep]

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

[spoiler]OA=E[/spoiler]

Solution:

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.

Alternate Solution:

Mary working together with Perry working at twice Mary’s rate is equivalent to three people working together at Mary’s rate. Since the job is finished in 20 minutes under these conditions, it takes Mary 3 x 20 = 60 minutes to finish the job alone.

Since Mary and Perry can finish the job together in 45 minutes, we have:

1/60 + 1/P = 1/45

1/P = 1/45 - 1/60

1/P = 4/180 - 3/180 = 1/180

So, working alone, Perry can finish the job in 180 minutes = 3 hours.

Answer: E