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Alex and Brenda both stand at point X. Alex begins to walk away from 15 May 2017, 10:43
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AdityaSurana94
Bunuel
enigma123
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).

Answer: C.

Hi bunuel..!
In this question why are we not considering it from Alex's point of view. I mean why not
2[4(t+1)]=Rt.?
I will be thankful if you clear my doubt.

Posted from my mobile device
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T in my solution is the time that Alex will have been walking when Brenda has covered twice as much distance as Alex because the question asks 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?

What is T in your solution?
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Alex and Brenda both stand at point X. Alex begins to walk away from 11 Dec 2017, 10:54
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enigma123
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
Show more

We are given that Alex has a rate of 4 mph and Brenda has a rate of R mph. We are also given that Alex begins to walk away from Brenda in a straight line at a rate of 4 mph. One hour later, Brenda begins to ride a bicycle in a straight line in the opposite direction. Thus, we can let Alex’s time = T + 1 and Brenda’s time = T.

Finally, since distance = rate x time, Alex’s distance = 4(T + 1) = 4T + 4 and Brenda’s distance = RT. We need to determine the amount of time it takes Brenda to cover twice the distance Alex has gone. So, we can create the following equation and determine T:

2(4T + 4) = RT

8T + 8 = RT

8 = RT - 8T

8 = T(R - 8)

8/(R - 8) = T

Since we are asked for Alex’s time, T + 1 = 8/(R - 8) + (R - 8)/(R - 8) = R/(R - 8).

Answer: C
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Alex and Brenda both stand at point X. Alex begins to walk away from 23 Oct 2020, 12:54
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Can this question be solved using the concept of relative speed?

Speed of B wrt A becomes (R+4) mph
Distance to be covered by B becomes (4+4)=8 miles

Hence time taken by A becomes 1+8/(R+4) hrs.

Could you please tell me what is it that I am doing wrong?
Thank you!

VeritasKarishma chetan2u Bunuel
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Alex and Brenda both stand at point X. Alex begins to walk away from 26 Oct 2020, 02:46
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pgwodehouse
Can this question be solved using the concept of relative speed?

Speed of B wrt A becomes (R+4) mph
Distance to be covered by B becomes (4+4)=8 miles

Hence time taken by A becomes 1+8/(R+4) hrs.

Could you please tell me what is it that I am doing wrong?
Thank you!

VeritasKarishma chetan2u Bunuel
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Note that A is continuously walking too. A doesn't stop after 1 hr. B has to cover twice the distance covered by A.
So B will cover the 4 miles that A has already covered while making up for all the distance being covered by A at that time and then cover more distance than A to cover twice the distance covered by A. So distance covered by B is much more than 8 miles. Also, (R + 4), the relative speed of B with respect to A would be relevant if we needed to do something about the total distance between them. But actually we need to compare distance covered by A with distance covered by B so their individual speeds are relevant. They could be walking in any direction - it wouldn't impact our answer.
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Alex and Brenda both stand at point X. Alex begins to walk away from 28 Feb 2021, 01:31
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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?

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).

Answer: C.
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Why have we multiplied T by 2 when we have already taken into account that T is the time taken by Alex covering double the distance covered by Brenda? Are we not double counting here?

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Alex and Brenda both stand at point X. Alex begins to walk away from 28 Feb 2021, 03:47
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mohammadfaraaz123
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enigma123
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).

Answer: C.



Why have we multiplied T by 2 when we have already taken into account that T is the time taken by Alex covering double the distance covered by Brenda? Are we not double counting here?

Posted from my mobile device
Show more

We are comparing distances here. We need such T that the distance covered by Alex in T hours, which is 4T, is half the distance covered by Brenda in (T - 1) hours, which is R(T-1). So, we need such T that satisfies 2*4T=R(T-1). As you can see there the distance covered by Alex in T hours, is half the distance covered by Brenda in (T - 1).
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Alex and Brenda both stand at point X. Alex begins to walk away from 30 Jul 2021, 06:16
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Marcab
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)
Show more

Even I was riddled with the same doubt. I understand it now!

If you take Brenda's time as (t) and Alex's time as (t+1), when you solve for "t", you shall get:

t = 8/(R-8). (Brenda's total time)

However, the question asks for Alex's total time for the distance covered.

Add +1 to both sides you shall get:

t+1 = 8/(R-8) +1 = (8 + R - 8)/(R - 8) -------> R/(R-8)

Therefore Answer (C).

Takeaway : Do not forget the perspective. Alex's time according to your approach is t+1 and not t. Hope this clarifies.
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Alex and Brenda both stand at point X. Alex begins to walk away from 06 Aug 2021, 09:59
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enigma123
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
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Let t be the requisite time then the eqn for the distance covered is given by

=>R*(T-1)=2*4T since b started one hour late

=>(R-8)*T=R

=>T=R/R-8

Therefore IMO C
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Alex and Brenda both stand at point X. Alex begins to walk away from 02 Sep 2021, 10:12
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enigma123
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
Show more

IMO C
Distance = Speed * Time
For A, distance = x ; Speed = 4 ; Time = x/4
For b, distance = 2x ; Speed = R ; Time = 2x/R

A started 1 hour early, so:
Time (A) - 1 = Time (B)
[x/4] - 1 = 2x/R
xR - 4R = 8x
x = 4R / [R-8]

Time (A) = x/4 = [4R / [R-8]] / 4
Time (A) = R/R-8
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Alex and Brenda both stand at point X. Alex begins to walk away from 17 Nov 2022, 01:29
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I think the easiest way to approach this problem is by taking numbers.
Let R = 16
When A could've been travelling for 2 hours (with 1 hour head start), A would've covered 8 miles. B, on the other hand, would've travelled twice as much, covering 16 miles in the opposite direction.
So, R = 16 in one of the five options should give you the answer as 2.
Only option C does.
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Alex and Brenda both stand at point X. Alex begins to walk away from 02 Feb 2023, 15:08
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Let time it will take for that to happen be y.


Alex time


y +1


Brenda's time

y


Distance covered within period

Alex

4(y+1)

4 + 4y

Brenda

Ry

So

Ry = 2(4+4y)

Ry = 8 + 8y

Ry - 8y =8

y = 8/R-8

But Alex time is y + 1

8/R -8 + 1

= R/R-8.

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Alex and Brenda both stand at point X. Alex begins to walk away from 23 Jun 2025, 07:43
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Distance of Alex= 4 * T-Alex
Distance of Brenda= R*T-Brenda

2* D-Alex= D-Brenda
Thus

8*T-Alex=R*T-Brenda
T-Alex=(R*T-Brenda)/8

Now what is T-Brenda, It is nothing but 1 Hour less from T-Alex since we know that Alex did a 1 hour heastart than Brenda

Thus T-Brenda becomes (T-Alex-1)

Substitutig this
T-Alex=R*(T-Alex-1)/8
8*TA= R(TA)-R
R=TA(R-8)
TA=R/(R-8)
enigma123
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
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Alex and Brenda both stand at point X. Alex begins to walk away from 29 Jul 2025, 11:34
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Hi Bunnel, can you please check what's wrong with my answer?

You considerd that the time spent by Brenda is (t-1) but I tried it by another way by assuming that Alex has already covered 4 miles for the 1 hour he walked before Brenda started to move so that equals to 4t+4

The time needed for Brenda to cover twice the distance covered by Alex = 2(4t+4)=RT .. 8T+8=RT >> RT-8T=8 so T(R-8)=8 >> T= 8/(R-8)
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enigma123
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).

Answer: C.
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Alex and Brenda both stand at point X. Alex begins to walk away from 30 Jul 2025, 01:38
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Andrew89
Hi Bunnel, can you please check what's wrong with my answer?

You considerd that the time spent by Brenda is (t-1) but I tried it by another way by assuming that Alex has already covered 4 miles for the 1 hour he walked before Brenda started to move so that equals to 4t+4

The time needed for Brenda to cover twice the distance covered by Alex = 2(4t+4)=RT .. 8T+8=RT >> RT-8T=8 so T(R-8)=8 >> T= 8/(R-8)
Bunuel
enigma123
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).

Answer: C.
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Your algebra is fine. The issue is the variable you solved for.

In your setup, t is Brenda’s riding time, so you got t = 8/(R-8). The question asks for Alex’s walking time. Since Alex started 1 hour earlier, T = t + 1. So T = 8/(R-8) + 1 = R/(R-8), which is choice C.
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