GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 21 Mar 2019, 09:16 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. ### Request Expert Reply # Aaron will jog from home at x miles per hour and then walk

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Manager  Joined: 04 Sep 2005
Posts: 128
Location: Fringes of the Boreal, Canada
Aaron will jog from home at x miles per hour and then walk  [#permalink]

### Show Tags

26 00:00

Difficulty:   25% (medium)

Question Stats: 77% (02:10) correct 23% (02:44) wrong based on 604 sessions

### HideShow timer Statistics

Aaron will jog from home at x miles per hour and then walk back home on 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

Originally posted by aikido_fudoshin on 29 Oct 2005, 16:08.
Last edited by Bunuel on 03 Feb 2015, 03:31, edited 2 times in total.
Edited the question and added the OA
Math Expert V
Joined: 02 Sep 2009
Posts: 53770
Re: Aaron will jog from home at x miles per hour and then walk  [#permalink]

### Show Tags

13
6
I'm lost with this question too. Can someone please explain? thanks!

Aaron will jog home at x miles per hour and then walk back home on 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.

Hope it helps.
_________________
##### General Discussion
Manager  Joined: 10 Sep 2005
Posts: 144
Re: Aaron will jog from home at x miles per hour and then walk  [#permalink]

### Show Tags

i dont know is this is a right approach...but try by plugging numbers
Let the total distance be : 100 km
Hypothetical
Speed Time (hrs)
Jogs : 50 kmph (X) 2
Walks : 20 kmph (Y) 5
------
7 (T)

try plugging in numbers...the ans should be 100
only XYT/(X + Y) = 100

hey! am just too absurd in my reasoning !!!!
Manager  Joined: 10 Sep 2005
Posts: 144
Re: Aaron will jog from home at x miles per hour and then walk  [#permalink]

### Show Tags

JUST BEING A BIT MORE CLEAR HERE...
i dont know is this is a right approach...but try by plugging numbers
Let the total distance be : 100 km
Hypothetical
Speed
Jogs : 50 kmph (X)
Walks : 20 kmph (Y)

Time
Jogs : 2 hrs
Walks : 5 hrs
------
Total : 7 hrs (T)

try plugging in numbers...the ans should be 100
only XYT/(X + Y) = 100

hey! am just too absurd in my reasoning !!!!
Senior Manager  Joined: 05 Oct 2005
Posts: 472
Re: Aaron will jog from home at x miles per hour and then walk  [#permalink]

### Show Tags

Is there another way to do this?? How does OG solve it ?

Thanks
Manager  Joined: 04 Sep 2005
Posts: 128
Location: Fringes of the Boreal, Canada
Re: Aaron will jog from home at x miles per hour and then walk  [#permalink]

### Show Tags

OA is C.

Here's how the OG solves it:

Add in the extra variable J to represent the # of hours Aaron spends jogging. Therefore,

XJ=distance jogged
Y(T-J)=distance walked

XJ=Y(T-J)
XJ=YT-JY
XJ + JY= YT
J(X+Y)=YT
J=YT/(X+Y)

# of miles he can jog is XJ therefore sub in YT/(X+Y) for J

=XYT/(X+Y)

I like the picking #'s approach better. Thanks!
Manager  Joined: 15 Apr 2011
Posts: 61
Re: Aaron will jog from home at x miles per hour and then walk  [#permalink]

### Show Tags

I'm lost with this question too. Can someone please explain? thanks!
_________________

Manager  Status: And the Prep starts again...
Joined: 03 Aug 2010
Posts: 104
Re: Aaron will jog from home at x miles per hour and then walk  [#permalink]

### Show Tags

I got the Distance as $$\frac{2XYt}{X+Y}$$

The logic I used was to find the average rates and then multiple it by time,t.

Average rates = $$\frac{2ab}{a+b}$$

where, a and b are the two given rates X and Y.

So, $$D= \frac{2XY}{X+Y}*t$$

What is the mistake here?
_________________

My First Blog on my GMAT Journey

Arise, Awake and Stop not till the goal is reached

Math Expert V
Joined: 02 Sep 2009
Posts: 53770
Re: Aaron will jog from home at x miles per hour and then walk  [#permalink]

### Show Tags

1
ENAFEX wrote:
I got the Distance as $$\frac{2XYt}{X+Y}$$

The logic I used was to find the average rates and then multiple it by time,t.

Average rates = $$\frac{2ab}{a+b}$$

where, a and b are the two given rates X and Y.

So, $$D= \frac{2XY}{X+Y}*t$$

What is the mistake here?

Not sure what are you doing in you solution. Why do you have 2 there? How did you get that the average rate is 2xy(x+y)?

Here is proper algebraic approach once more:

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: $$\frac{d}{x}+\frac{d}{y}=t$$ --> $$d(\frac{1}{x}+\frac{1}{y})=t$$ --> $$d=\frac{xyt}{x+y}$$.

Please study it and tell me if you see a problem there.
_________________
Manager  Status: And the Prep starts again...
Joined: 03 Aug 2010
Posts: 104
Re: Aaron will jog from home at x miles per hour and then walk  [#permalink]

### Show Tags

$$Average Rate=\frac{total distance}{total time}$$
$$Total Time= \frac{d}{a}+\frac{d}{b}$$
$$Average Rate= \frac{d+d}{\frac{d}{a}+\frac{d}{b}} = \frac{2d}{\frac{d(a+b)}{ab}} =\frac{2ab}{a+b}$$

something similar to the problem below.

http://gmatclub.com/forum/average-rate-on-round-trip-85218.html
_________________

My First Blog on my GMAT Journey

Arise, Awake and Stop not till the goal is reached

Math Expert V
Joined: 02 Sep 2009
Posts: 53770
Re: Aaron will jog from home at x miles per hour and then walk  [#permalink]

### Show Tags

1
ENAFEX wrote:
$$Average Rate=\frac{total distance}{total time}$$
$$Total Time= \frac{d}{a}+\frac{d}{b}$$
$$Average Rate= \frac{d+d}{\frac{d}{a}+\frac{d}{b}} = \frac{2d}{\frac{d(a+b)}{ab}} =\frac{2ab}{a+b}$$

something similar to the problem below.

http://gmatclub.com/forum/average-rate-on-round-trip-85218.html

I see. The point is that $$\frac{2xyt}{x+y}$$ is the total distance, meaning that it's the distance for the round trip and we are asked to find only one way distance (how many miles from home can Aaron jog), which would be half of this value so $$\frac{xyt}{x+y}$$.

Hope it's clear.
_________________
Intern  Joined: 26 Jan 2015
Posts: 4
Re: Aaron will jog from home at x miles per hour and then walk  [#permalink]

### Show Tags

Hay i always hear that there are small tricks gmac puts in to help figure out problems..

the trick i used for this problem: In all the other answer miles/hour is being added to hours. since they dont have the same unit you cant add them together, only multiply therefore all the answers with (x + t) or ( y + t) can not be correct and there is only one that is in the correct format
SVP  Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1817
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: Aaron will jog from home at x miles per hour and then walk  [#permalink]

### Show Tags

2
aikido_fudoshin wrote:
Aaron will jog home at x miles per hour and then walk back home on 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

Can someone please update the question......

Aaron will jog from home
_________________

Kindly press "+1 Kudos" to appreciate Intern  Joined: 23 Jun 2011
Posts: 18
Concentration: Finance, Other
WE: Information Technology (Health Care)
Re: Aaron will jog from home at x miles per hour and then walk  [#permalink]

### Show Tags

Hey Bunuel,

I have a query.. i solved this question by checking units.. Please tell is this the right way.. Through this was i solved it in 7-8 seconds..else question might take more time.. plz tell if my process is right or wrong?

Aaron will jog from home at x miles per hour and then walk back home on 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

As i saw only in C we have (speed^2 )* time / speed = distance..

No other option comply the rule of unit..
VP  D
Joined: 09 Mar 2016
Posts: 1275
Re: Aaron will jog from home at x miles per hour and then walk  [#permalink]

### Show Tags

Bunuel wrote:
I'm lost with this question too. Can someone please explain? thanks!

Aaron will jog home at x miles per hour and then walk back home on 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.

Hope it helps.

Hello Bunuel can you please rephrase the question "How many miles from home can Aaron jog so that he spends a total of t hours jogging and walking?"

I simply could not understand what this question want ? Total distance done by walking and jogging ? thanks Math Expert V
Joined: 02 Sep 2009
Posts: 53770
Re: Aaron will jog from home at x miles per hour and then walk  [#permalink]

### Show Tags

1
dave13 wrote:
Bunuel wrote:
I'm lost with this question too. Can someone please explain? thanks!

Aaron will jog home at x miles per hour and then walk back home on 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.

Hope it helps.

Hello Bunuel can you please rephrase the question "How many miles from home can Aaron jog so that he spends a total of t hours jogging and walking?"

I simply could not understand what this question want ? Total distance done by walking and jogging ? thanks Say the distance in d miles. Aaron jogs d miles at x mile/hour and then walks back the same d miles at y mile/hour. So, Aaron spends on jogging d/x hours and on walking d/y hours, so total time (from home jogging and back walking) takes him t = d/x + d/y hours.

Now, the question asks to find the distance (d) Aaron jogs (How many miles from home can Aaron jog). So, basically the question asks to express d in terms of x, y, and t.

Hope it's clear.
_________________ Re: Aaron will jog from home at x miles per hour and then walk   [#permalink] 04 Jul 2018, 11:28
Display posts from previous: Sort by

# Aaron will jog from home at x miles per hour and then walk

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.  