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Aaron travels from town x to town y and then back from town y to town

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Aaron travels from town x to town y and then back from town y to town  [#permalink]

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New post 10 Oct 2018, 12:35
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Difficulty:

  45% (medium)

Question Stats:

69% (01:43) correct 31% (02:37) wrong based on 79 sessions

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Aaron travels from town X to town Y and then back from town Y to town X, taking different routes in each direction. If his speed when travelling from town X to town Y is 36 miles per hour, and his speed when travelling in the opposite direction is 48 miles per hour, what is his average speed for the entire journey?

1) The length of the return trip is 24% of the entire distance traveled.

2) The length of the return trip is 100 miles.

*I noted difficulty as 600-700. Maybe it is 700. Please let me know what you think the difficulty should be.
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Re: Aaron travels from town x to town y and then back from town y to town  [#permalink]

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New post 10 Oct 2018, 14:11
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philipssonicare wrote:
Aaron travels from town X to town Y and then back from town Y to town X, taking different routes in each direction. If his speed when travelling from town X to town Y is 36 miles per hour, and his speed when travelling in the opposite direction is 48 miles per hour, what is his average speed for the entire journey?

1) The length of the return trip is 24% of the entire distance traveled.

2) The length of the return trip is 100 miles.

*I noted difficulty as 600-700. Maybe it is 700. Please let me know what you think the difficulty should be.


D1 = T1 * V1
T1 = D1/V1

Avg speed = (Total distance)/(Total time)

Statement one tells us that D1 = 0.24Dtotal

D1 + D2 = Dtotal

0.24Dtotal + D2 = Dtotal

D2 = 0.76Dtotal.

T1 = 0.24Dtotal/36

T2 = 0.76Dtotal/48

Avg speed = Dtotal/ (T1+T2)


1 equation 1 variable we can find the answer

A is sufficient

Statement 2

gives us D2 but that is not enough to find anything.
Insufficient

Posted from my mobile device
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Re: Aaron travels from town x to town y and then back from town y to town  [#permalink]

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New post 11 Oct 2018, 15:40
3
Nice solution Salsanousi.
I've elaborated below so that others can see "1 equation 1 variable we can find the answer" (as I certainly didn't when I started).

Average speed = \(\frac{Total Distance}{Total Time}\)
D1T1V1 and D2T2V2 6 variables
D1T136mph and D2T248mph 4 unknown variables (speed taken from the original condition)

1)0.76D, T1, 36mph and 0.24D, T2, 48mph
T=\(\frac{D}{V}\)

T1=\(\frac{0.76D}{36}\)

T2=\(\frac{0.24D}{48}\)

Now we have the respective Ts. Want to find the respective Ds
D1=36·\(\frac{0.76D}{36}\)=36·0.76D

D2=48·\(\frac{0.24D}{48}\)=48·0.24D

Average speed = \(\frac{Total Distance}{Total Time}\)

Average speed = \(\frac{36·0.76D+48·0.24D}{\frac{0.76D}{36}+\frac{0.24D}{48}}\)

Multiply through by 100 to get rid of the decimals

=\(\frac{3600·76D+4800·24D}{\frac{76D}{3600}+\frac{24D}{4800}}\)

Simplify the denominator

=\(\frac{\frac{D(3600·76+4800·24)}{1}}{\frac{47D}{1800}}\)

=\(\frac{1800D(3600·76+4800·24)}{47D}\)

Cancel D from the numerator and denominator

=\(\frac{1800(3600·76+4800·24)}{47}\)

Shows that average speed is a number, we just don't need to work out what that number is.
Sufficient
AD

2) D1T136mph and D2100miles48mph 3 unknown variables
We can't solve for 3 unknown variables with one equation


Anyone that reads this answer, kudos please! It took me over half an hour with all of the formatting!
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Aaron travels from town x to town y and then back from town y to town  [#permalink]

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New post Updated on: 11 Oct 2018, 16:00
philipssonicare

Thanks glad it could help.

By the way in your elaborated solution you added some extra steps that can be avoided.

For avg speed it will be = Dtotal/(0.24Dtotal/36 + 0.76Dtotal/48)

the only variable in here is Dtotal which cancels out.

What you did was to multiply V1 * T1 and also V2 * T2 to get Dtotal. This extra step can be avoided. I hope it makes sense and is clear

I apologize for my formatting as I solved the question using the mobile, I will edit it later from the computer.

Posted from my mobile device

Originally posted by Salsanousi on 11 Oct 2018, 15:54.
Last edited by Salsanousi on 11 Oct 2018, 16:00, edited 1 time in total.
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Re: Aaron travels from town x to town y and then back from town y to town  [#permalink]

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New post 11 Oct 2018, 15:58
Salsanousi your formatting is fine
I was simply going out of my way to try to make it as clear as possible
Thanks once again for your input
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Re: Aaron travels from town x to town y and then back from town y to town   [#permalink] 11 Oct 2018, 15:58
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Aaron travels from town x to town y and then back from town y to town

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