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

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

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]
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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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

Project PS Butler : Question #51

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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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.

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

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?

one may even ignore taking the LCM in this case, and just multiply each of the three ratios by 3, to make it a whole number ratio...

1/3*3 : 1*3 : 3*3
1 : 3 : 9 option (C)
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Re: Three automobiles travel distances that are in the ratios of 1:2:3. [#permalink]
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Re: Three automobiles travel distances that are in the ratios of 1:2:3. [#permalink]
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