Alex and Brenda both stand at point X. Alex begins to walk away from

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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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.

So, you just have to add 1 to your result to get the correct answer:
8 / (R - 8) +1 = (8 + R - 8) / (R - 8) = R / ( R - 8).
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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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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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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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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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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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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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Very clear and concise explanation, thank you.

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 R2 – 4

Solution - Lets assume Alex travels X miles when Brenda begins to ride. Then,

Time taken by Alex = Time taken by Brenda
X/4 = [(X+4)2]/R --- since Brenda covers twice as distance as Alex in total thus Brenda distance is (X+4)2

which gives X = 32/(R-8)

Now time taken by Alex = X/4 = [32/(R-8)]/4 = 8/(R-8)

WHERE DID I GO WRONG ? Answer is C, not D

Hi,
The Q seems more on lines of IIM CAT than GMAT..
your solution is correct, except the last step..
x/4 is the time, both have travelled ..
But Alex had already travelled 1 hr prior to that..
so Alex time is x/4 +1= 8/(R-8) +1..
{8 + (R-8)}/(R-8) =R/(R-8)..

choice D is given to force students to make errors..

Hope it helped
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HI ravi007shankar,

This question should probably be posted in the PS Forum here:

gmat-problem-solving-ps-140/

Here's how you can solve this question by TESTing VALUES:

We're told that 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 (and that R > 8). We're asked 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.

Let's TEST R = 12

After 1 hour....
Alex = 4 miles walked
Brenda = 0 miles biked

After 2 hours...
Alex = 8 miles walked
Brenda = 12 miles biked

After 3 hours...
Alex = 12 miles walked
Brenda = 24 miles biked
This is a MATCH for what we were told, so we're looking for an answer that equals 3 when R=12. There's only one answer that matches...

Final Answer:

GMAT assassins aren't born, they're made,
Rich
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the wording is indeed confusing...and one might get messy with all the VIC's...
My approach, assign variables:
we need to find the time of A, when B covered twice the distance A covered.
since R>8, suppose R=9.
when alex covered 4 miles, brenda covered 0 - 1hour
when alex covered 8 miles, brenda - 9 miles - 2 hours
when alex covered 12 miles, brenda - 18 miles - 3 hours
when alex covered 16 miles, brenda covered - 27 miles - 4 hours
when alex covered 20 miles, brenda - 36 miles - 5 hours
when alex covered 24 miles, brenda - 45 miles - 6 hours
when alex covered 28 miles, brenda - 54 miles - 7 hours
when alex covered 32 miles, brenda - 63 miles - 8 hours
when alex covered 36 miles, brenda - 72 miles - AHA, we have 2X the distance. time - 9 hours.

ok, so when R=9, time must be 9.
now plug in values:

A R – 4 = 9-4=5 - out
B R / (R + 4) - 9/13 - out
C R / (R – 8) = 9/1 = 9 works, let's see other options
D 8 / (R – 8) = 8/-1 = -8
E R2 – 4 = 18-4=14 - nope.

C alone works. thus, C is the answer.

p.s. I see Rich is more experienced with testing values..he picked the numbers way better than me, and saved a lot of time

Hi mvictor,

You saw the opportunity to TEST VALUES, which is good. The next 'step' in your training should be to spot the 'clues' in the prompt that can help you to pick the most efficient VALUES to TEST. In the answer choices, you should notice all of the '4s' and '8s' - implying that multiples of 4 will likely be useful here. When combined with the fact that Alex is walking 4 miles/hour and Brenda's speed has to be GREATER than 8, the number 12 seems like a really logical choice.

GMAT assassins aren't born, they're made,
Rich
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Answer: Option D


Check the solution in attachment

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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.

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