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# 3 machines have a productivity ratio of 1 to 2 to 5. All 3

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3 machines have a productivity ratio of 1 to 2 to 5. All 3 [#permalink]

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16 Feb 2011, 04:34
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3 machines have a productivity ratio of 1 to 2 to 5. All 3 machines are working on a job for 3 hours. At the beginning of the 4th hour, the slowest machine breaks. It is fixed at the beginning of hour seven, and begins working again. The job is done in nine hours. What was the ratio of the work performed by the fastest machine as compared to the slowest?

A. 5
B 7
C 15/2
D 17/2
E 12
[Reveal] Spoiler: OA

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Re: 3 machines have a productivity ratio of 1 to 2 to 5. All 3 [#permalink]

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16 Feb 2011, 07:50
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3 machines have a productivity ratio of 1:2:5. all 3 machines are working on a job for 3 hours. at the beginning of the 4th hour, the slowest machine breaks. it is fixed at the beginning at hour 7, and begins working again. the job is done in 9 hours. what was the ratio of the work performed by the fastest machine to the work performed by the slowest?

"3 machines have a productivity ratio of 1:2:5" means that in a time interval (1 hour, 1 year, ...) the first machine can produce 1 part (so it's the slowest one), the second can produce 2 parts and the third and fastest one can produce 5 parts.

Now, the fastest machine worked for whole 9 hours thus produced 9*5=45 parts but the slowest machine worked only for 6 hours thus produced 6*1=6 parts, so the ratio of the work performed by the fastest machine to the work performed by the slowest is 45/6=15/2.
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Re: 3 machines have a productivity ratio of 1 to 2 to 5. All 3 [#permalink]

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16 Feb 2011, 04:49
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1:2:5

Let's consider 1 work is done by the slowest machine in 1 hour.

in first 3 hours; Work performed by 3 machines
1*3:2*3:5*3

From beginning of 4th hour until start of 7th hour, 3 hours elapsed. Work performed by 3 machines
0:2*3:5*3. First one is 0 work as it is broken.

Job is done in nine hours; from start of 7th hour until end of 9th hour, 3 hours elapsed. Work performed by 3 machines
1*3:2*3:5*3

Total work performed by slowest machine: 3+3=6
Total work performed by fastest machine: 15+15+15=45

Ratio = 45/6 = 15/2

Ans: 15/2
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Re: 3 machines have a productivity ratio of 1 to 2 to 5. All 3 [#permalink]

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11 Aug 2011, 06:02
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ruturaj wrote:
please explain how slowest machine works for 6 hours

slowest machine worked
1st hour
2nd hour
3rd hour
Got broken
got fixed and returned to work at the beginning of the 7th hour so:
7th hour
8th hour
9th hour

Total of 6 hours.

So the slowest machine made 6 pieces, while the fastest machine made 45
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Re: 3 machines have a productivity ratio of 1 to 2 to 5. All 3 [#permalink]

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17 Feb 2011, 12:45
thanks for posting +1
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Re: 3 machines have a productivity ratio of 1 to 2 to 5. All 3 [#permalink]

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11 Aug 2011, 05:27
please explain how slowest machine works for 6 hours
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Re: 3 machines have a productivity ratio of 1 to 2 to 5. All 3 [#permalink]

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11 Aug 2011, 08:02
ruturaj wrote:
please explain how slowest machine works for 6 hours

3 machines have a productivity ratio of 1:2:5. all 3 machines are working on a job for 3 hours. at the beginning of the 4th hour, the slowest machine breaks. it is fixed at the beginning at hour 7, and begins working again. the job is done in 9 hours. what was the ratio of the work performed by the fastest machine to the work performed by the slowest?

Productivity ratio of 1:2:5 means;

In 1 hour:
Slowest machine just finishes 1 work
Medium fast machine finishes 2 work
Fastest machine finishes 5 work

3 hours work:
Slowest: 3*1=3 work
Medium: 3*2=6 work
Fastest: 3*5=15 work

THEN SLOWEST BREAKS.
It misses(3 hours):
4th hour
5th hour
6th hour

During which:
Medium fast completes: 3*2=6 work
Fastest completes: 3*5=15 work

Then
7th, 8th, 9th hour(3 hours)
Slowest: 3*1=3 work
Medium: 3*2=6 work
Fastest: 3*5=15 work

Work by fastest:Work by slowest
15+15+15:3+3
45:6
15:2
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Re: 3 machines have a productivity ratio of 1 to 2 to 5. All 3 [#permalink]

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12 Aug 2011, 00:22
0-1 fastest = 5 slowest = 1
1-2----5----------1 ----
2-3 fastest = 5 ----1---

6-7----5--------1--
7-8----5---------1--
8-9----5---------1--

hence total = 45 and 6

thus 15/2
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Re: 3 machines have a productivity ratio of 1 to 2 to 5. All 3 [#permalink]

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12 Aug 2011, 02:03
+1 for explanation..
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Re: 3 machines have a productivity ratio of 1 to 2 to 5. All 3 [#permalink]

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21 Aug 2011, 10:37
let's suppose that in 1 hour each machine produces 1+2+5 = 8 units

in 3 hrs = 24 units
next 3 hrs = 21 units (slowest isnt working)
further 3 hrs = 24 untis

fastest worked for 9 hours, while the slowest worked for 6 hrs.

units produced by fastest / units produced by slowest = 9*5/6*1 = 15/2
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Re: 3 machines have a productivity ratio of 1 to 2 to 5. All 3 [#permalink]

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21 Aug 2011, 14:29
Let M1 be the slowest and M3 be the fastest machine.

<---first 3 hours--><----3 hours----><---3 hours---->

M1 M1
M2 M2 M2
M3 M3 M3

productivity ratio = 1:2:5 (which is per hour)

x: 2x: 5x

work done by M3/ work done by M1 = (9*5x) / (6*x) = 45/6 = 15/2
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Re: 3 machines have a productivity ratio of 1 to 2 to 5. All 3 [#permalink]

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02 Dec 2012, 22:49
The productivity ratio of the fastest machine to the slowest machine is 5:1.

The fastest machine worked for 9 straight hours. Thus, W = 5 x 9 = 45
The slowest machine brokedown in the 4th hour and was revived on the 7th hour. Thus, W = 1 x 6 = 6

The Output Ratio of fastest to slowest is 45 is to 6 ==> 15 : 2
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Re: 3 machines have a productivity ratio of 1 to 2 to 5. All 3 [#permalink]

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05 Jan 2017, 15:19
Let's say the productivity ratio refers to how many units each produces in 1 hour. The fastest (most productive) machine works for 9 hours and makes 5 per hour, totally 45 units. The slowest (least productive) machine works for 6 hours and produces 1 per hour for a total of 6. Thus, the ratio of units produced fast/slow is 45/6 or 15/2. No more math required
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Re: 3 machines have a productivity ratio of 1 to 2 to 5. All 3 [#permalink]

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05 Jan 2017, 17:19
GMATD11 wrote:
3 machines have a productivity ratio of 1 to 2 to 5. All 3 machines are working on a job for 3 hours. At the beginning of the 4th hour, the slowest machine breaks. It is fixed at the beginning of hour seven, and begins working again. The job is done in nine hours. What was the ratio of the work performed by the fastest machine as compared to the slowest?

A. 5
B 7
C 15/2
D 17/2
E 12

fastest machine's work=9hrs*5 units per hr=45 total units
slowest machine's work=6 hrs*1 unit per hr=6 total units
45/6=15/2
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3 machines have a productivity ratio of 1 to 2 to 5. All 3 [#permalink]

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09 Apr 2017, 14:25
Common sense solution:

Ratio of work is 1:2:5

Meaning: As Bunuel defined "in a time interval (1 hour, 1 year, ...) the first machine can produce 1 part (so it's the slowest one), the second can produce 2 parts and the third and fastest one can produce 5 parts."

Time progression:

Hour 1: 1:2:5 parts produced
Hour 2: 2:4:10 parts produced
Hour 3: 3:6:15 parts produced
Hour 4: 3:8:20 parts produced //Machine 1 breaks, produces no more parts
Hour 5: 3:10:25 parts produced
Hour 6: 3:12:30 parts produced
Hour 7: 4:14:35 parts produced //Machine 1 is fixed, continues to produce parts
Hour 8: 5:16:40 parts produced
Hour 9: 6:18:45 parts produced //Job done

So when looking at the final tally of parts produced in 9 hours, the fastest machine produced 45 parts and the slowest produced only 6. Reducing this ratio we get 15/2.
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Re: 3 machines have a productivity ratio of 1 to 2 to 5. All 3 [#permalink]

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12 Apr 2017, 09:55
The productivity ratios are 1:2:5. Let's assume that the basic rate is x. So rates are 1x:2x:5x.
The fastes machine worked 9 hours, therefore it did 9/1x work. The slowest machine didn't work from 4th to 6th hours so were broken for 3 hours. Therefore the work done by this machine is 6/5x.
Let's compare work done by both machines: (9/1x)/(6/5x)=(9/x)*(5x/6)=15/2
Re: 3 machines have a productivity ratio of 1 to 2 to 5. All 3   [#permalink] 12 Apr 2017, 09:55
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