A Manhattan Challenege Problem ---Two Contradicting Answers

[Saurabh Malpani]

Hello,
The following Challenege problem was published on 01/09/2006. With My apporach (I don't find anything wrong) I get answer as D but with your apporach (Which is also not wrong) I get C. My apporach is given at the end of the Problem ..Please clarify that that why do we have two contradicting answers.

01/09/06
Question
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


Answer
If we want Brenda's distance to be twice as great as Alex's distance, we can set up the following equation:

2(4T) = R(T - 1), where 4T is Alex's distance (rate × time) and R(T - 1) is Brenda's distance (since Brenda has been traveling for one hour less).

If we simplify this equation to isolate the T (which represents Alex's total time), we get:

2(4T) = R(T - 1)
8T = RT - R
R = RT - 8T
R = T(R - 8)
R /(R - 8) = T

This is choice C

My Apporach

T is the time breda bkies for.
In the first hour Alex covers 4 miles.

So we can that
Distance covered by Alex = 4+4T
Distance Covered by Breda is= RT

we are given that 2(4+4T) =RT
8+8T=RT

8=T(R-8)

[u]T= 8/(R-8)[/u]

[Saurabh Malpani]

I guess some problem I have edited the post ------- The following is the correct post (hope so)

Hello,
The following Challenege problem was published on 01/09/2006. With My apporach (I don't find anything wrong) I get answer as D but with your apporach (Which is also not wrong) I get C. My apporach is given at the end of the Problem ..Please clarify that that why do we have two contradicting answers.

01/09/06
Question
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) R^2 - 4


Answer
If we want Brenda's distance to be twice as great as Alex's distance, we can set up the following equation:

2(4T) = R(T - 1), where 4T is Alex's distance (rate × time) and R(T - 1) is Brenda's distance (since Brenda has been traveling for one hour less).

If we simplify this equation to isolate the T (which represents Alex's total time), we get:

2(4T) = R(T - 1)
8T = RT - R
R = RT - 8T
R = T(R - 8 )
R /(R - 8 ) = T

This is choice C

My Apporach

T is the time breda bkies for.
In the first hour Alex covers 4 miles.

So we can that
Distance covered by Alex = 4+4T
Distance Covered by Breda is= RT

we are given that 2(4+4T) =RT
8+8T=RT

8=T(R- 8 )

T= 8/(R- 8 )

[StaceyKoprince]

So close! But you did make a mistake here - the problem asks for Alex's time and you solved for Brenda's time. (Remember, in your set-up, you set the variable T to equal Brenda's time.)

If T = 8/(r- 8 ) and Alex went for an hour more, we have to add 1: T = [8/(r-8 )] + 1
Then get a common denominator so you can add the two:
T = 8/(r-8 ) + (r-8 )/(r-8 )
T = (8+r-8 )/(r-8 )
T = r/(r-8 )
answer = C

In problems like this one, they'll always give you the other person's time or distance or whatever in the answer choices - so always double check to make sure you're solving for what they want.

ETA: apparently an 8 immediately followed by a ) is a shortcut for one of the smiley face emoticons. 8) If you need to use this combo for an actual math problem, just put a space between - as in 8 )

[Saurabh Malpani]

Hey Stacey,

Thank you very Much absolutely Great!!!----

I see where the problem ..I will log this in my Log book....this is what I am trying to avoid Silly mistakes on my Exams!!!!


Thank you very much once again!!!! It really helped!