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If five machines working at the same rate can do 3/4 of a job in 30min

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If five machines working at the same rate can do 3/4 of a job in 30min [#permalink]

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Q: If five machines working at the same rate can do \(\frac{3}{4}\) of a job in 30 minutes, how many minutes would it take two machines working at the same rate to do \(\frac{3}{5}\) of the job?

(A) 45
(B) 60
(C) 75
(D) 80
(E) 100

Could someone help with this please? Thank you!
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If five machines working at the same rate can do 3/4 of a job in 30min [#permalink]

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blokker wrote:
Q: If five machines working at the same rate can do \(\frac{3}{4}\) of a job in 30 minutes, how many minutes would it take two machines working at the same rate to do \(\frac{3}{5}\) of the job?

(A) 45
(B) 60
(C) 75
(D) 80
(E) 100

Could someone help with this please? Thank you!


hi,

find working rate from " five machines working at the same rate can do \(\frac{3}{4}\) of a job in 30 minutes"
5* machines does 3/4 job in 30 min

so 1* machine will do 3/4 job in 30*5 min
and 1* machine will do full job in \(30*5*\frac{4}{3}=200\) min

so 2* machine- full job in \(\frac{200}{2}=100\) min
finally 2* machine will do \(\frac{3}{5}\) job in \(100*\frac{3}{5}=60\)min
ans 60 min B

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Re: If five machines working at the same rate can do 3/4 of a job in 30min [#permalink]

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New post 21 Mar 2016, 05:17
using the std formula
m1d1h1/w1=m2d2h2/w2
substituting the values we have

5*1/2*4/3=2*5/3*x (converted 30 min into hours =1/2)
10/3=10/3*x
x=1 hour
so 60 minutes
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Re: If five machines working at the same rate can do 3/4 of a job in 30min [#permalink]

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New post 21 Mar 2016, 05:25
blokker wrote:
Q: If five machines working at the same rate can do \(\frac{3}{4}\) of a job in 30 minutes, how many minutes would it take two machines working at the same rate to do \(\frac{3}{5}\) of the job?

(A) 45
(B) 60
(C) 75
(D) 80
(E) 100

Could someone help with this please? Thank you!


If 5 MACHINES can do 3/4 of a job in 30 MIN, 5 MACHINES will do the hole job in 40 MIN (3/4 ----->30 MIN 4/4 -----> X)

NOW: 5 MACHINES DO THE HOLE JOB BY A RATE OF 1/A EACH MACHINE ----> 5*1/A= 1 HOLE JOB/40 MIN -----> THEREFORE THE RATE OF 1 MACHINE TO DO THE HOLE JOB IS 1/200 OR 200 MINS.

NOW TO CALCULATE THE JOB OF 2 MACHINES TO DO 3/5 OF THE JOB:

2 MACHINES WITH A RATE OF 1/200 TO DO 3/5 OF THE JOB---> 2*1/200=3/5 OF THE JOB / X MIN

THEREFORE WE HAVE 1/100 / 3/5 * XMIN -----> 5 * XMIN = 300 ----> XMIN= 300/5= 60 MIN
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Re: If five machines working at the same rate can do 3/4 of a job in 30min [#permalink]

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New post 21 Jun 2017, 05:24
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Re: If five machines working at the same rate can do 3/4 of a job in 30min [#permalink]

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New post 21 Jun 2017, 05:42
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blokker wrote:
Q: If five machines working at the same rate can do \(\frac{3}{4}\) of a job in 30 minutes, how many minutes would it take two machines working at the same rate to do \(\frac{3}{5}\) of the job?

(A) 45
(B) 60
(C) 75
(D) 80
(E) 100

Could someone help with this please? Thank you!

Breakdown and solve
Quote:
If five machines working at the same rate can do \(\frac{3}{4}\) of a job in 30 minutes

Time required for 5 machines to do the complete work is 30*4/3 = 40 min
Time required for 1 machines to do the complete work is 40*5 = 200 mins

Quote:
how many minutes would it take two machines working at the same rate to do \(\frac{3}{5}\) of the job?

\(=\frac{200}{2}*\frac{3}{5}\)
= \(60 \ min\)

Thus, answer will be (B) 60 Min

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Re: If five machines working at the same rate can do 3/4 of a job in 30min [#permalink]

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New post 22 Jun 2017, 16:16
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blokker wrote:
Q: If five machines working at the same rate can do \(\frac{3}{4}\) of a job in 30 minutes, how many minutes would it take two machines working at the same rate to do \(\frac{3}{5}\) of the job?

(A) 45
(B) 60
(C) 75
(D) 80
(E) 100

Could someone help with this please? Thank you!

Attachment:
numberwrt.jpg
numberwrt.jpg [ 83.8 KiB | Viewed 839 times ]


Manhattan Prep sometimes uses the following formula for multiple workers:

Work = Number of Workers x Individual Rate x Time

Add one extra column, Number of Workers, to the very straightforward RTW table.

Writing this method out makes it look hard. It isn't. And it's fast. It took me 41 seconds.

Simply manipulate the W = (# * RATE * TIME) formula, just as if it were without the extra factor.

W = Work
# = # of workers
R = individual rate
T = time


Solving with rates and time in hours first. See top table.

"[F]ive machines working at the same rate can do \(\frac{3}{4}\) of a job in 30 minutes..." 30 minutes = \(\frac{1}{2}\)hour

1. We need an individual rate, which will be used to find time taken in Case 2.

Just from manipulating the formula: individual Rate, R is \(\frac{W}{(# * T)}\)

2. Calculate denominator first: (# * T)

= 5 * \(\frac{1}{2}\) = \(\frac{5}{2}\)

3. Find individual rate -- \(\frac{W}{(# * T)}\)

\(\frac{3}{4}\) ÷ \(\frac{5}{2}\) =

\(\frac{3}{4} * \frac{2}{5}\) =

\(\frac{3}{10}\) = Individual rate (amount of work per hour)

4. How much time will it take "two machines working at the same rate to do \(\frac{3}{5}\) of the job?"

T =\(\frac{W}{(# * R)}\)

Denominator first: 2 * \(\frac{3}{10}\) =

\(\frac{6}{10}\) = \(\frac{3}{5}\)

Find time: \(\frac{3}{5}\) ÷ \(\frac{3}{5}\) =

\(\frac{3}{5}\) * \(\frac{5}{3}\) = 1

1 hour = 60 minutes

Solving with time and rates in minutes, see second table

1. We need individual worker's rate, which will be used to calculate time in Case 2

\(\frac{W}{(# * T)}\) = Individual Rate, R

2. Calculate denominator first: (# * T) =

5 * 30 = 150

3. Find individual rate -- \(\frac{W}{(# * T)}\)

\(\frac{3}{4}\) ÷ 150 = \(\frac{3}{4}\)* \(\frac{1}{150}\)= \(\frac{3}{600}\) =

\(\frac{1}{200}\) = Individual Rate in amount of work per minute

4. Find time for Case 2. "How many minutes would it take two machines working at the same rate to do \(\frac{3}{5}\) of the job?"

T = \(\frac{W}{(# * R)}\)

Denominator first: 2 * \(\frac{1}{200}\) = \(\frac{2}{200}\) = \(\frac{1}{100}\)

Time = \(\frac{3}{5}\) ÷ \(\frac{1}{100}\) =

\(\frac{3}{5}\) * \(\frac{100}{1}\) =

\(\frac{300}{5}\) = 60 minutes

Answer B
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Re: If five machines working at the same rate can do 3/4 of a job in 30min [#permalink]

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New post 23 Jun 2017, 09:29
blokker wrote:
Q: If five machines working at the same rate can do \(\frac{3}{4}\) of a job in 30 minutes, how many minutes would it take two machines working at the same rate to do \(\frac{3}{5}\) of the job?

(A) 45
(B) 60
(C) 75
(D) 80
(E) 100


let m=minutes needed
rate of 1 machine=1/(5*40)=1/200
m*2*1/200=3/5
m=60 minutes
B
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Re: If five machines working at the same rate can do 3/4 of a job in 30min [#permalink]

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New post 23 Jun 2017, 10:01
rate of 1 machine = 3/(4*30*5) = 1/200,
minutes*2*1/200 = 3/5,
minutes = 60,
answer = B
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If five machines working at the same rate can do 3/4 of a job in 30min [#permalink]

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New post 17 Jul 2017, 07:19
blokker wrote:
Q: If five machines working at the same rate can do \(\frac{3}{4}\) of a job in 30 minutes, how many minutes would it take two machines working at the same rate to do \(\frac{3}{5}\) of the job?

(A) 45
(B) 60
(C) 75
(D) 80
(E) 100

Could someone help with this please? Thank you!


\(5\) machines can do \(\frac{3}{4}\) of a job in \(30\) mins.

Therefore, Time required for \(5\) machines to finish the job \(= 30*\frac{4}{3} => 40\) mins

Therefore, Time required for \(1\) machine to finish the job \(= 40*5 => 200\) mins

Time required for \(2\) machines to finish the job \(= \frac{200}{2} => 100\) mins

Therefore, Time required for \(2\) machines to do \(\frac{3}{5}\) of the job \(= \frac{3}{5} * 100 = 3 * 20 = 60\) mins.

Answer (B)...
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Re: If five machines working at the same rate can do 3/4 of a job in 30min [#permalink]

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New post 01 Aug 2017, 23:41
Bunuel Can you please let me know as to where am i going wrong in my concept . Thank you.
Number of machine =5
And 5 machines can do ¾ (Total work)
Therefore, the total work = # of machines*total time=total work
5*30=150 units
¾(150)=112.5 units
Therefore, 2 machines can do 3/5 (150)=90 units
2*x minutes =90
Therefore the total minutes = 90/2= 45 minutes.
Here in where am I going wrong??
Re: If five machines working at the same rate can do 3/4 of a job in 30min   [#permalink] 01 Aug 2017, 23:41
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