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# Aaron will jog from home at x miles per hour

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Aaron will jog from home at x miles per hour [#permalink]

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20 Sep 2010, 08:35
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Aaron will jog from home at x miles per hour and then walk back home by the same route at y miles per hour. How many miles from home can Aaron jog so that he spends a total of t hours jogging and walking?

A) xt/y
B) (x+t)/xy
C) xyt/(x+y)
D) (x+y+t)/xy
E) ((y+t)/x)-(t/y)

OPEN DISCUSSION OF THIS QUESTION IS HERE: aaron-will-jog-home-at-x-miles-per-hour-and-then-walk-back-22234.html
[Reveal] Spoiler: OA

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Re: OG Algebra [#permalink]

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20 Sep 2010, 08:47
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Q-1) Aaron will jog from home at x miles per hour and then walk back home by the same route at y miles per hour. How many miles from home can Aaron jog so that he spends a total of t hours jogging and walking?

Let the no.of miles Aaron covers be D.

Total Time = Time (jogging) + Time (Walking)
t hours = D/x + D/y
t = D ((x+y)/xy)
D = xyt/(x+y)

So the answer is C.
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Re: OG Algebra [#permalink]

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20 Sep 2010, 09:02
The question is asking for a general answer in terms of other variables. It is not a great technique to substitute values to get an answer, because depending on what values you plug in, you might actually get two or more hits in the answers.

The question is straight forwards enough. If the total distance he goes is m miles, then the time he takes is :

m/x(going) + m/y(coming) = t

So m = xyt/(x+y)
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Re: OG Algebra [#permalink]

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20 Sep 2010, 09:33
greatchap wrote:
Query: we know that he will jog for 4 miles. So what does ques mean How many miles from home can Aaron jog so that he spends a total of t hours jogging and walking?
If the ques asked how many miles can he walk then also the answer would be the same as distance from home and back is same.

Kinda confused a bit.

Can anyone clarify this ques a bit ?

Thanks,

GR

You are right answer would be the same, as the question basically asks about the distance in miles of one-way route from home to some point, where he stops jogging turns and returns back home walking.
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Re: OG Algebra [#permalink]

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20 Sep 2010, 11:01
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greatchap wrote:
Q-1) Aaron will jog from home at x miles per hour and then walk back home by the same route at y miles per hour. How many miles from home can Aaron jog so that he spends a total of t hours jogging and walking?

a) xt/y ---------> unit of time , this can not be the answer
b) x+t/xy ---------> you can not add speed and time
c) xyt/x+y ----------> unit of distance, this could be the answer
d) (x+y+t)/xy -----------> you can not add speed and time
e) ((y+t)/x)-(t/y) -------->can not add speed and time

Hence C

This is basically physics' concept of DIMENSIONS.

Otherwise shrouded1 gave nice explanation. Follow it.
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Re: OG Algebra [#permalink]

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20 Sep 2010, 18:09
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I used the way siyer and others solved. Gurpreet reminded of nice physics dimenstions concept where we used to calculate the units in [M], [L], [T] etc
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Re: OG Algebra [#permalink]

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21 Sep 2010, 08:00
Thanks a lot guys. I understood it now. I appreciate your help.

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Solving OG12 Diagnostic V24 - Alternative solution [#permalink]

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01 Oct 2010, 08:09
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Hi,

I'd like to share with you an alternative and very powerful technique for solving hard to grasp questions. These type of questions show up from time to time and this technique saved my ass when I was blocked, so it might help you out.

This technique is an ancient one I learned 11 years ago in my Physics class. I'll show you how to use it on a sample problem taken from OG12, diagnostic test question 24 somehow edited:

Quote:
Young padawan will jog from Yoda's training camp at x miles per hour and then walk back to the camp at y miles per hour. How many miles from the camp can padawan jog so that he spends a total of t hours jogging and walking?

A) xt/y

B) (x+t)/y

C) xyt/(x+y)

D) (x+y+t)/(xy)

E) (y+t)/x - t/y

If you don't know how to algebraically solve the problem, the trick is to analyze the units in the answer choices, let's see if they are homogeneous.

x and y are speeds so their units are [distance / time]

A) yields a time, which is incorrect as we are looking for a distance.

B) is illegal, as we can't add a speed to a time.

C) yields a distance, so it could be the correct answer.

D) is illegal as we can't add speeds to a time

E) is illegal as we can't add a speed to a time.

Therefore answer C is correct.

Obviously if another answer looked like (xyt)/(x-y) then this trick wouldn't work as two (or more) answer choices would remain. But I noticed that for these questions, if you analyze the units, usually only one answer choice has the homogeneous units.

Keep me updated if this trick helped you out

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Re: Solving OG12 Diagnostic V24 - Alternative solution [#permalink]

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01 Oct 2010, 08:35
Thanks for sharing, but it has been already discussed.

Check out !!

og-algebra-101376.html#p785205
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Re: Solving OG12 Diagnostic V24 - Alternative solution [#permalink]

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01 Oct 2010, 08:47

As the other poster did not correctly title his thread, I was not able to find it. This thread can therefore be locked.

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Re: OG Algebra [#permalink]

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25 Mar 2014, 10:05
Bunuel wrote:
greatchap wrote:
Query: we know that he will jog for 4 miles. So what does ques mean How many miles from home can Aaron jog so that he spends a total of t hours jogging and walking?
If the ques asked how many miles can he walk then also the answer would be the same as distance from home and back is same.

Kinda confused a bit.

Can anyone clarify this ques a bit ?

Thanks,

GR

You are right answer would be the same, as the question basically asks about the distance in miles of one-way route from home to some point, where he stops jogging turns and returns back home walking.

Bunuel,

Can you pls help in clearing my doubt about where am I doing wrong in this problem. I have considered Total Distance/Total Speed=Time(T), So 2D/x+y=T. I am struck. pls clear my doubt.

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Re: OG Algebra [#permalink]

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02 Apr 2014, 00:07
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anu1706 wrote:
Bunuel wrote:
greatchap wrote:
Query: we know that he will jog for 4 miles. So what does ques mean How many miles from home can Aaron jog so that he spends a total of t hours jogging and walking?
If the ques asked how many miles can he walk then also the answer would be the same as distance from home and back is same.

Kinda confused a bit.

Can anyone clarify this ques a bit ?

Thanks,

GR

You are right answer would be the same, as the question basically asks about the distance in miles of one-way route from home to some point, where he stops jogging turns and returns back home walking.

Bunuel,

Can you pls help in clearing my doubt about where am I doing wrong in this problem. I have considered Total Distance/Total Speed=Time(T), So 2D/x+y=T. I am struck. pls clear my doubt.

I'm not Bunuel, however would like to reply:

There cannot be "total speed" by adding two different speeds in this problem

However, we can say Total Time = Time required in Jogging + Time required in Walking

$$t = \frac{d}{x} + \frac{d}{y}$$

$$t = \frac{d (x+y)}{xy}$$

$$d = \frac{xyt}{(x+y)}$$

One more method:

Say time required in Jogging = q
So time required in walking = (t-q)

Forming the equations to find distance d

d = xq

$$q = \frac{d}{x}$$ ........... (1)

d = y(t-q) .......... (2)

Substitute value of q in equation (2)

$$d = y(t-\frac{d}{x})$$

$$d + \frac{yd}{x} = yt$$

$$d (1+\frac{y}{x}) = yt$$

$$d = \frac{ytx}{(x+y)} = Answer$$
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Re: OG Algebra [#permalink]

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02 May 2014, 03:03
gurpreetsingh wrote:
greatchap wrote:
Q-1) Aaron will jog from home at x miles per hour and then walk back home by the same route at y miles per hour. How many miles from home can Aaron jog so that he spends a total of t hours jogging and walking?

a) xt/y ---------> unit of time , this can not be the answer
b) x+t/xy ---------> you can not add speed and time
c) xyt/x+y ----------> unit of distance, this could be the answer
d) (x+y+t)/xy -----------> you can not add speed and time
e) ((y+t)/x)-(t/y) -------->can not add speed and time

Hence C

This is basically physics' concept of DIMENSIONS.

Otherwise shrouded1 gave nice explanation. Follow it.

Dimensional analysis made it easier and quicker

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Re: Aaron will jog from home at x miles per hour [#permalink]

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02 May 2014, 03:07
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Aaron will jog from home at x miles per hour and then walk back home by the same route at y miles per hour. How many miles from home can Aaron jog so that he spends a total of t hours jogging and walking?

A) xt/y
B) (x+t)/xy
C) xyt/(x+y)
D) (x+y+t)/xy
E) ((y+t)/x)-(t/y)

Algebraic approach:

Say the distance Aaron jogs is $$d$$ miles, notice that the distance Aaron walks back will also be $$d$$ miles (since he walks back home on the same route).

Next, total time $$t$$ would be equal to the time he spends on jogging plus the time he spends on walking: $$\frac{d}{x}+\frac{d}{y}=t$$ --> $$d(\frac{1}{x}+\frac{1}{y})=t$$ --> $$d=\frac{xyt}{x+y}$$.

Number picking approach:

Say the distance in 10 miles, $$x=10$$ mile/hour and $$y=5$$ mile/hour (pick x and y so that they will be factors of 10).

So, Aaron spends on jogging 10/10=1 hour and on walking 10/5=2 hours, so total time $$t=1+2=3$$ hours.

Now, we have that $$x=10$$, $$y=5$$ and $$t=3$$. Plug these values into the answer choices to see which gives 10 miles. Only answer choice C fits: $$\frac{xyt}{x+y}=\frac{10*5*3}{10+5}=10$$.

Note that for plug-in method it might happen that for some particular number(s) more than one option may give "correct" answer. In this case just pick some other numbers and check again these "correct" options only.

OPEN DISCUSSION OF THIS QUESTION IS HERE: aaron-will-jog-home-at-x-miles-per-hour-and-then-walk-back-22234.html
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Re: Aaron will jog from home at x miles per hour   [#permalink] 02 May 2014, 03:07
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