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Three automobiles travel distances that are in the ratios of 1:2:3.

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Three automobiles travel distances that are in the ratios of 1:2:3.  [#permalink]

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New post 01 Dec 2018, 09:06
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Three automobiles travel distances that are in the ratios of 1:2:3. If the ratios of the traveling times over these distances for these automobiles are 3:2:1 in the same respective order, what are the ratios of their respective average speeds?

(A) 1:1:1
(B) 1:3:3
(C) 1:3:9
(D) 3:2:1
(E) 3:4:3

Project PS Butler : Question #51


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Re: Three automobiles travel distances that are in the ratios of 1:2:3.  [#permalink]

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New post 01 Dec 2018, 09:20
1
Distance Ratio = 1x:2x:3x

Time taken ratio = 3x:2x:1x

Average speed = Total Distance/Time = 1/3 : 2/2 : 3/1
Taking LCM gives 1:3:9.

C is the answer.
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Re: Three automobiles travel distances that are in the ratios of 1:2:3.  [#permalink]

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New post 04 Dec 2018, 04:26
Afc0892 wrote:
Distance Ratio = 1x:2x:3x

Time taken ratio = 3x:2x:1x

Average speed = Total Distance/Time = 1/3 : 2/2 : 3/1
Taking LCM gives 1:3:9.

C is the answer.



Can you explain this a little further? How did you figure out you need to get the LCM? Also, how did you come up with the final ratio?
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Re: Three automobiles travel distances that are in the ratios of 1:2:3.  [#permalink]

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New post 04 Dec 2018, 04:31
justgottamakeit1592 wrote:
Afc0892 wrote:
Distance Ratio = 1x:2x:3x

Time taken ratio = 3x:2x:1x

Average speed = Total Distance/Time = 1/3 : 2/2 : 3/1
Taking LCM gives 1:3:9.

C is the answer.



Can you explain this a little further? How did you figure out you need to get the LCM? Also, how did you come up with the final ratio?


The ratio is 1/3 : 1 : 3/1
Since this option is not listed in the answer choices. We need to further simplify.
Now,
LCM of denominator is 3.
Now multiply the ratio by 3, we get

1/3*3 : 1*3 : 3/1*3
1:3:9

Hope it's clear

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Re: Three automobiles travel distances that are in the ratios of 1:2:3.  [#permalink]

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New post 04 Dec 2018, 04:35
Ahh I see..thanks for the quick response!
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Re: Three automobiles travel distances that are in the ratios of 1:2:3.  [#permalink]

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New post 23 Jan 2019, 09:46
HKD1710 wrote:
Three automobiles travel distances that are in the ratios of 1:2:3. If the ratios of the traveling times over these distances for these automobiles are 3:2:1 in the same respective order, what are the ratios of their respective average speeds?

(A) 1:1:1
(B) 1:3:3
(C) 1:3:9
(D) 3:2:1
(E) 3:4:3

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Lets solve this problem by taking examples:

Distances are in the ratio --> 1:2:3
i.e.
Da = 100Kms
Db = 200Kms
Dc = 300Kms

Times are in the ratio --> 3:2:1
i.e.
Ta = 3 hours
Tb = 2 hours
Tc = 1 hour

Now:
Sa = 100kms/3 hours = 33.33 Kmph
Sb = 200kms/2 hours = 100 Kmph
Sc = 300kms/3 hours = 300kmph

Now Sa:Sb:Sc = 33.33:100:300 = 1:3:9

Hence C is the correct option
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Re: Three automobiles travel distances that are in the ratios of 1:2:3.  [#permalink]

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New post 27 Jan 2019, 19:18
HKD1710 wrote:
Three automobiles travel distances that are in the ratios of 1:2:3. If the ratios of the traveling times over these distances for these automobiles are 3:2:1 in the same respective order, what are the ratios of their respective average speeds?

(A) 1:1:1
(B) 1:3:3
(C) 1:3:9
(D) 3:2:1
(E) 3:4:3


We can let the distance traveled by the three automobiles be 30, 60, and 90, and the traveling times be 3, 2 and 1, respectively. Thus, the average speeds are 30/3 = 10, 60/2 = 30, and 90/1 = 90, respectively. Therefore, the ratios of their respective average speeds are 10:30:90 or 1:3:9.

Answer: C
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Re: Three automobiles travel distances that are in the ratios of 1:2:3.   [#permalink] 27 Jan 2019, 19:18
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