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# Alex and Brenda both stand at point X. Alex begins to walk a

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Alex and Brenda both stand at point X. Alex begins to walk a [#permalink]

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07 Mar 2012, 18:17
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Alex and Brenda both stand at point X. Alex begins to walk away from Brenda in a straight line at a rate of 4 miles per hour. One hour later, Brenda begins to ride a bicycle in a straight line in the opposite direction at a rate of R miles per hour. If R > 8, which of the following represents the amount of time, in terms of R, that Alex will have been walking when Brenda has covered twice as much distance as Alex?

A. R-4
B. R/(R+4)
C. R/(R-8)
D. 8/(R-8)
E. 2R - 4

Guys - I don't have an OA for this. Can you please help in terms of how this can be solved?
[Reveal] Spoiler: OA

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Last edited by Bunuel on 18 Jul 2013, 12:21, edited 2 times in total.

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Re: Alex and Brenda both stand at point X. Alex begins to walk a [#permalink]

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07 Mar 2012, 22:43
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enigma123 wrote:
Alex and Brenda both stand at point X. Alex begins to walk away from Brenda in a straight line at a rate of 4 miles per hour. One hour later, Brenda begins to ride a bicycle in a straight line in the opposite direction at a rate of R miles per hour. If R > 8, which of the following represents the amount of time, in terms of R, that Alex will have been walking when Brenda has covered twice as much distance as Alex?

A. R-4
B. R/R+4
C. R/R-8
D. 8/R-8
E. 2R - 4

Guys - I don't have an OA for this. Can you please help in terms of how this can be solved?

Let T be the time that Alex will have been walking when Brenda has covered twice as much distance as Alex.

In T hours Alex will cover 4T miles;
Since Brenda begins her journey 1 hour later than Alex then total time for her will be T-1 hours, and the distance covered in that time will be R(T-1);

We want the distance covered by Brenda to be twice as much as that of Alex: 2*4T=R(T-1) --> 8T=RT-R --> T=R/(R-8).

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Re: Alex and Brenda both stand at point X. Alex begins to walk a [#permalink]

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07 Mar 2012, 23:59
Bunuel wrote:
enigma123 wrote:
Alex and Brenda both stand at point X. Alex begins to walk away from Brenda in a straight line at a rate of 4 miles per hour. One hour later, Brenda begins to ride a bicycle in a straight line in the opposite direction at a rate of R miles per hour. If R > 8, which of the following represents the amount of time, in terms of R, that Alex will have been walking when Brenda has covered twice as much distance as Alex?

A. R-4
B. R/R+4
C. R/R-8
D. 8/R-8
E. 2R - 4

Guys - I don't have an OA for this. Can you please help in terms of how this can be solved?

Let T be the time that Alex will have been walking when Brenda has covered twice as much distance as Alex.

In T hours Alex will cover 4T miles;
Since Brenda begins her journey 1 hour later than Alex then total time for her will be T-1 hours, and the distance covered in that time will be R(T-1);

We want the distance covered by Brenda to be twice as much as that of Alex: 2*4T=R(T-1) --> 8T=RT-R --> T=R/(R-8).

Hi Bunuel,

I tried with a different method but my answer is different .. I am sure I am doing some error but i am not able to find where my folly is:

Let X be the distance Alex covers:
Time taken by Alex: X/4
Brenda's distance should be 2X
Time taken by Brenda: 2X/R

Given: Time taken by Alex + 1 = Time taken by Brenda
X/4 + 1 = 2X/R
X = 4R/8-R

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Re: Alex and Brenda both stand at point X. Alex begins to walk a [#permalink]

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08 Mar 2012, 00:10
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Expert's post
rohitgoel15 wrote:
Bunuel wrote:
enigma123 wrote:
Alex and Brenda both stand at point X. Alex begins to walk away from Brenda in a straight line at a rate of 4 miles per hour. One hour later, Brenda begins to ride a bicycle in a straight line in the opposite direction at a rate of R miles per hour. If R > 8, which of the following represents the amount of time, in terms of R, that Alex will have been walking when Brenda has covered twice as much distance as Alex?

A. R-4
B. R/R+4
C. R/R-8
D. 8/R-8
E. 2R - 4

Guys - I don't have an OA for this. Can you please help in terms of how this can be solved?

Let T be the time that Alex will have been walking when Brenda has covered twice as much distance as Alex.

In T hours Alex will cover 4T miles;
Since Brenda begins her journey 1 hour later than Alex then total time for her will be T-1 hours, and the distance covered in that time will be R(T-1);

We want the distance covered by Brenda to be twice as much as that of Alex: 2*4T=R(T-1) --> 8T=RT-R --> T=R/(R-8).

Hi Bunuel,

I tried with a different method but my answer is different .. I am sure I am doing some error but i am not able to find where my folly is:

Let X be the distance Alex covers:
Time taken by Alex: X/4
Brenda's distance should be 2X
Time taken by Brenda: 2X/R

Given: Time taken by Alex + 1 = Time taken by Brenda
X/4 + 1 = 2X/R
X = 4R/8-R

We are asked to find the time that Alex will have been walking and you found X, which is the distance that Alex have covered.

So, you need to take the last step: Time=Distance/Rate=(4R/(8-R))/4=R/(8-R).

Hope it's clear.
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Re: Alex and Brenda both stand at point X. Alex begins to walk a [#permalink]

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08 Mar 2012, 05:16
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enigma123 wrote:
Alex and Brenda both stand at point X. Alex begins to walk away from Brenda in a straight line at a rate of 4 miles per hour. One hour later, Brenda begins to ride a bicycle in a straight line in the opposite direction at a rate of R miles per hour. If R > 8, which of the following represents the amount of time, in terms of R, that Alex will have been walking when Brenda has covered twice as much distance as Alex?

A. R-4
B. R/R+4
C. R/R-8
D. 8/R-8
E. 2R - 4

Guys - I don't have an OA for this. Can you please help in terms of how this can be solved?

Since your answer is in terms of R, you have the flexibility of putting in any value for R.
Say R = 16
Alex has already covered 4 miles in the first hour. In the next hour, Alex covers another 4 miles while Brenda covers 16, thereby covering twice the distance covered by Alex. (I chose R = 16 because it is twice of 8) Alex has been walking for 2 hrs so that's the answer we are looking for.
Plug R = 16 in the options. Only option C gives you 2. Answer (C)
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Re: Alex and Brenda both stand at point X. Alex begins to walk a [#permalink]

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04 Sep 2012, 11:51
Can you please let me know where am I committing mistake?
Alex already covered 4 miles. In the next t hours the total distance covered by Alex will be 4+4t.
Similarly Brenda covers Rt miles in the next t hours.
Therefore, Rt=2(4+4t)t
t=8/(R-8)
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Re: Alex and Brenda both stand at point X. Alex begins to walk a [#permalink]

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04 Sep 2012, 13:05
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siddharthasingh wrote:
Can you please let me know where am I committing mistake?
Alex already covered 4 miles. In the next t hours the total distance covered by Alex will be 4+4t.
Similarly Brenda covers Rt miles in the next t hours.
Therefore, Rt=2(4+4t)t
t=8/(R-8)

The question is "which of the following represents the amount of time, in terms of R, that Alex will have been walking when Brenda has covered twice as much distance as Alex?"

Your t is the time Brenda rode her bicycle and t + 1 is the time Alex walked.

8 / (R - 8) +1 = (8 + R - 8) / (R - 8) = R / ( R - 8).
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Re: Alex and Brenda both stand at point X. Alex begins to walk a [#permalink]

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26 Sep 2012, 19:10
Bunuel wrote:
enigma123 wrote:
Alex and Brenda both stand at point X. Alex begins to walk away from Brenda in a straight line at a rate of 4 miles per hour. One hour later, Brenda begins to ride a bicycle in a straight line in the opposite direction at a rate of R miles per hour. If R > 8, which of the following represents the amount of time, in terms of R, that Alex will have been walking when Brenda has covered twice as much distance as Alex?

A. R-4
B. R/R+4
C. R/R-8
D. 8/R-8
E. 2R - 4

Guys - I don't have an OA for this. Can you please help in terms of how this can be solved?

Let T be the time that Alex will have been walking when Brenda has covered twice as much distance as Alex.

In T hours Alex will cover 4T miles;
Since Brenda begins her journey 1 hour later than Alex then total time for her will be T-1 hours, and the distance covered in that time will be R(T-1);

We want the distance covered by Brenda to be twice as much as that of Alex: 2*4T=R(T-1) --> 8T=RT-R --> T=R/(R-8).

Hi Bunuel,

I worked the problem until I got to 8T = RT - R but I started struggling with the algebra. Can you show me how you manipulated the equation to get T = R/(R-8)?

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Re: Alex and Brenda both stand at point X. Alex begins to walk a [#permalink]

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27 Sep 2012, 00:10
egiles wrote:
Bunuel wrote:
enigma123 wrote:
Alex and Brenda both stand at point X. Alex begins to walk away from Brenda in a straight line at a rate of 4 miles per hour. One hour later, Brenda begins to ride a bicycle in a straight line in the opposite direction at a rate of R miles per hour. If R > 8, which of the following represents the amount of time, in terms of R, that Alex will have been walking when Brenda has covered twice as much distance as Alex?

A. R-4
B. R/R+4
C. R/R-8
D. 8/R-8
E. 2R - 4

Guys - I don't have an OA for this. Can you please help in terms of how this can be solved?

Let T be the time that Alex will have been walking when Brenda has covered twice as much distance as Alex.

In T hours Alex will cover 4T miles;
Since Brenda begins her journey 1 hour later than Alex then total time for her will be T-1 hours, and the distance covered in that time will be R(T-1);

We want the distance covered by Brenda to be twice as much as that of Alex: 2*4T=R(T-1) --> 8T=RT-R --> T=R/(R-8).

Hi Bunuel,

I worked the problem until I got to 8T = RT - R but I started struggling with the algebra. Can you show me how you manipulated the equation to get T = R/(R-8)?

8T = RT - R ----> R = RT - 8T (added R and subtracted 8T from both sides) ----> R = T(R - 8) ----> T = R/(R - 8)
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Re: Alex and Brenda both stand at point X. Alex begins to walk a [#permalink]

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27 Sep 2012, 04:15
egiles wrote:
Bunuel wrote:
enigma123 wrote:
Alex and Brenda both stand at point X. Alex begins to walk away from Brenda in a straight line at a rate of 4 miles per hour. One hour later, Brenda begins to ride a bicycle in a straight line in the opposite direction at a rate of R miles per hour. If R > 8, which of the following represents the amount of time, in terms of R, that Alex will have been walking when Brenda has covered twice as much distance as Alex?

A. R-4
B. R/R+4
C. R/R-8
D. 8/R-8
E. 2R - 4

Guys - I don't have an OA for this. Can you please help in terms of how this can be solved?

Let T be the time that Alex will have been walking when Brenda has covered twice as much distance as Alex.

In T hours Alex will cover 4T miles;
Since Brenda begins her journey 1 hour later than Alex then total time for her will be T-1 hours, and the distance covered in that time will be R(T-1);

We want the distance covered by Brenda to be twice as much as that of Alex: 2*4T=R(T-1) --> 8T=RT-R --> T=R/(R-8).

Hi Bunuel,

I worked the problem until I got to 8T = RT - R but I started struggling with the algebra. Can you show me how you manipulated the equation to get T = R/(R-8)?

Sure:

8T=RT-R --> rearrange: R=RT-8T --> factor out T: R=T(R-8) --> T=R/(R-8).

Hope it's clear.
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Re: Alex and Brenda both stand at point X. Alex begins to walk a [#permalink]

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30 Sep 2012, 04:47
In such questions i am trying to find smart number to plug in, so for R i am chosing 12 (which is easily dividible to 4). We know that Alex walked for 1 hour that is 4 miles, then Brenda started to bike, so in 1 our she bikes 12 miles, and Alex will walk overall 8 miles, next hour Alex will walk 12 miles Brenda bikes 24 miles (which is twice of the alex's distance). Overall Alex spends 3 hours of walking. Now we look at the answer choices, and put 12 instead of R and the answer should be 3 and we see that answer C fits. So the answer is C.
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Re: Alex and Brenda both stand at point X. Alex begins to walk a [#permalink]

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06 Oct 2012, 00:36
VeritasPrepKarishma wrote:
enigma123 wrote:
Alex and Brenda both stand at point X. Alex begins to walk away from Brenda in a straight line at a rate of 4 miles per hour. One hour later, Brenda begins to ride a bicycle in a straight line in the opposite direction at a rate of R miles per hour. If R > 8, which of the following represents the amount of time, in terms of R, that Alex will have been walking when Brenda has covered twice as much distance as Alex?

A. R-4
B. R/R+4
C. R/R-8
D. 8/R-8
E. 2R - 4

Guys - I don't have an OA for this. Can you please help in terms of how this can be solved?

Since your answer is in terms of R, you have the flexibility of putting in any value for R.Say R = 16
Alex has already covered 4 miles in the first hour. In the next hour, Alex covers another 4 miles while Brenda covers 16, thereby covering twice the distance covered by Alex. (I chose R = 16 because it is twice of 8) Alex has been walking for 2 hrs so that's the answer we are looking for.
Plug R = 16 in the options. Only option C gives you 2. Answer (C)

Hi Karishma,

Suppose i assume R=32,
then alex = 4m/hr. In next hr, Alex covers 4 and brenda covers 2*16
In next hr, Alex covers 8 and brenda covers 2*32 and so on.. but acc to the series i cannot be that when Brenda wud be covering 2(Alex) ?
Can you please have a look on this ?

Thanks

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Re: Alex and Brenda both stand at point X. Alex begins to walk a [#permalink]

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06 Oct 2012, 20:46
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154238 wrote:
VeritasPrepKarishma wrote:
enigma123 wrote:
Alex and Brenda both stand at point X. Alex begins to walk away from Brenda in a straight line at a rate of 4 miles per hour. One hour later, Brenda begins to ride a bicycle in a straight line in the opposite direction at a rate of R miles per hour. If R > 8, which of the following represents the amount of time, in terms of R, that Alex will have been walking when Brenda has covered twice as much distance as Alex?

A. R-4
B. R/R+4
C. R/R-8
D. 8/R-8
E. 2R - 4

Guys - I don't have an OA for this. Can you please help in terms of how this can be solved?

Since your answer is in terms of R, you have the flexibility of putting in any value for R.Say R = 16
Alex has already covered 4 miles in the first hour. In the next hour, Alex covers another 4 miles while Brenda covers 16, thereby covering twice the distance covered by Alex. (I chose R = 16 because it is twice of 8) Alex has been walking for 2 hrs so that's the answer we are looking for.
Plug R = 16 in the options. Only option C gives you 2. Answer (C)

Hi Karishma,

Suppose i assume R=32,
then alex = 4m/hr. In next hr, Alex covers 4 and brenda covers 2*16
In next hr, Alex covers 8 and brenda covers 2*32 and so on.. but acc to the series i cannot be that when Brenda wud be covering 2(Alex) ?
Can you please have a look on this ?

Thanks

If you assume R = 32, in 2 hrs, Alex covers 8 miles and Brenda covers 32 miles. Brenda has already covered more than twice of Alex. Hence, somewhere within the second hour, Brenda had covered twice the distance covered by Alex. To find it, you will anyway need to make equations.
Say t is the time for which they travel after Alex's initial 4 miles.
2(4 + 4t) = 32t
t = 1/3
So total time for which Alex walked = 1 + 1/3 = 4/3

Now put R = 32 in the options and you get t = 4/3 in case of option (C)

The point is, it's too much work in this case. If you assume the value smartly, your work reduces significantly else you might as well use algebra.
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Re: Alex and Brenda both stand at point X. Alex begins to walk a [#permalink]

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15 Oct 2012, 17:10
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Solving Duration : 30 secs
Solving Method : Substitute Assumption

Explanation:

Given : Speed of Alex = 4 miles/hr
Speed of Brenda= R > 8 miles/hr

Assume, Speed of Brenda = 16 [I choose a substitute which is divisible by 4 and 8 ]

At end of 1st hour, distance traveled by Alex = 4
distance traveled by Brenda = 0

At end of 2nd hour, distance traveled by Alex = 8
distance traveled by Brenda = 16 [where distance traveled by Brenda is twice the distance traveled by Alex]

Therefore, Substituting the value of R as 16 in the equation, we get option C as answer.

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Re: Alex and Brenda both stand at point X. Alex begins to walk a [#permalink]

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18 Jul 2013, 12:16
I tried number plugging in this question. Let's say R = 10, now Alex has already been walking for an hour so he has already completed a distance of 4 miles. Brenda starts an hour later, in one hour after Brenda's start she will have completed 10 miles and Alex will have completed 8 miles.
2 hours later, Brenda = 20 miles, Alex = 12 miles.
3 hours later, Brenda = 30 miles, Alex = 16 miles.
4 hours later, Brenda = 40 miles, Alex = 20 miles. We stop here

Now since Brenda started an hour later, this means in 5 hours, Brenda will have traveled double of Alex's distance.

The only answer that gives us 5 when we plug 10 for R is (C), R/R-8 => 10/(10-8) = 10/2 = 5.

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Re: Alex and Brenda both stand at point X. Alex begins to walk a [#permalink]

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03 Aug 2013, 10:51
Alex and Brenda both stand at point X. Alex begins to walk away from Brenda in a straight line at a rate of 4 miles per hour. One hour later, Brenda begins to ride a bicycle in a straight line in the opposite direction at a rate of R miles per hour. If R > 8, which of the following represents the amount of time, in terms of R, that Alex will have been walking when Brenda has covered twice as much distance as Alex?

We know Alex's rate (4 miles/hour)
We know Brenda's rate is greater than 8 (8 miles/hour)

In one hour Alex will have covered four miles. In two hours, Alex will have covered eight miles. When Alex has covered exactly four miles Brenda will set off at a rate of 8+ miles/hour.
It may be easier to plug in numbers for this problem.

R=12

This means that in two hours Alex will cover 8 miles and Brenda will cover 12. In three hours Alex will cover 12 miles and Brenda will cover 24. The answer must = 3.

R/(R-8)
12/(12-8)
12/4
=3 hours

Solving another way:

T = the time Alex will have walked when Brenda covers twice the distance (what the question is looking for)

Alex is traveling at 4 miles/hour so in T hours Alex will cover 4T miles. Rate*time = distance she covers

Brenda left one hour after Alex so her time will be T-1. The distance she covers will therefore be R(T-1). We are looking for how long it takes Brenda to cover two times the distance Alex does.

We need to know how long (T) it will take for Brenda to cover twice the distance Alex has covered: 2*(4T) = R(T-1) ==> 8T = RT-R ==> 8t+R=RT

There are two T's here so arrange the equation in such a way to factor them out.

8T+R=RT
R=RT-8T
R=T(R-8)
We are looking for the solution in terms of R: T=R/(R-8) (C)

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Re: Alex and Brenda both stand at point X. Alex begins to walk a [#permalink]

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04 Nov 2013, 14:39
Bunuel wrote:
enigma123 wrote:
Alex and Brenda both stand at point X. Alex begins to walk away from Brenda in a straight line at a rate of 4 miles per hour. One hour later, Brenda begins to ride a bicycle in a straight line in the opposite direction at a rate of R miles per hour. If R > 8, which of the following represents the amount of time, in terms of R, that Alex will have been walking when Brenda has covered twice as much distance as Alex?

A. R-4
B. R/R+4
C. R/R-8
D. 8/R-8
E. 2R - 4

Guys - I don't have an OA for this. Can you please help in terms of how this can be solved?

Let T be the time that Alex will have been walking when Brenda has covered twice as much distance as Alex.

In T hours Alex will cover 4T miles;
Since Brenda begins her journey 1 hour later than Alex then total time for her will be T-1 hours, and the distance covered in that time will be R(T-1);

We want the distance covered by Brenda to be twice as much as that of Alex: 2*4T=R(T-1) --> 8T=RT-R --> T=R/(R-8).

Hi Bunuel,

Would you tell where am I going wrong in my approach.
Distance by alex in 1hr = 1*4 = 4 miles.
Now, let 't' be the time at which distance covered by brenda= 2*distance covered by alex

R*t = 2*(4+4t)
solving the above equation, t comes out to be 8/(R-8)

Thanks.

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Re: Alex and Brenda both stand at point X. Alex begins to walk a [#permalink]

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05 Nov 2013, 07:11
ankit41 wrote:
Bunuel wrote:
enigma123 wrote:
Alex and Brenda both stand at point X. Alex begins to walk away from Brenda in a straight line at a rate of 4 miles per hour. One hour later, Brenda begins to ride a bicycle in a straight line in the opposite direction at a rate of R miles per hour. If R > 8, which of the following represents the amount of time, in terms of R, that Alex will have been walking when Brenda has covered twice as much distance as Alex?

A. R-4
B. R/R+4
C. R/R-8
D. 8/R-8
E. 2R - 4

Guys - I don't have an OA for this. Can you please help in terms of how this can be solved?

Let T be the time that Alex will have been walking when Brenda has covered twice as much distance as Alex.

In T hours Alex will cover 4T miles;
Since Brenda begins her journey 1 hour later than Alex then total time for her will be T-1 hours, and the distance covered in that time will be R(T-1);

We want the distance covered by Brenda to be twice as much as that of Alex: 2*4T=R(T-1) --> 8T=RT-R --> T=R/(R-8).

Hi Bunuel,

Would you tell where am I going wrong in my approach.
Distance by alex in 1hr = 1*4 = 4 miles.
Now, let 't' be the time at which distance covered by brenda= 2*distance covered by alex

R*t = 2*(4+4t)
solving the above equation, t comes out to be 8/(R-8)

Thanks.

Your T and T in the solution are not the same.
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Re: Alex and Brenda both stand at point X. Alex begins to walk a [#permalink]

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05 Nov 2013, 08:16
I arbitrarily picked R = 12

After 1 hour, Alex will have walked 4 miles. For each our after that, his total distance d = 4t + 4, where t is the number of hours he walks.

Brenda walks twice that distance in 2d = 12t or d = 6t.

Now just set them equal to each other

4t + 4 = 6t
2t = 4
t = 2

Add the additional hour that Alex was walking in the beginning, so t = 3. Just plug in 12 to all of the answer choices and see which one yields 3. C.

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Re: Alex and Brenda both stand at point X. Alex begins to walk a [#permalink]

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26 Nov 2013, 04:03
Hi,

I tried using this method:

let T be the time Brenda has to travel in order to cover twice the distance that Alex does:

So,

Distance (Brenda) = 2 Distance(Alex)
Speed of Brenda * T = 2 [ 4*T + 4 ] (the additional 4 miles covered in initial hour)
R * T = 8T + 8
T (R-8) = 8
T = 8 / (R-8) (C)

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Re: Alex and Brenda both stand at point X. Alex begins to walk a   [#permalink] 26 Nov 2013, 04:03

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