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# One hour after Yolanda started walking from X to Y, a

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Intern
Joined: 20 Dec 2005
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One hour after Yolanda started walking from X to Y, a [#permalink]  05 Jan 2006, 16:41
12. One hour after Yolanda started
walking from X to Y, a distance of 45
miles, Bob started walking along the
same road from Y to X. If Yolandaâ€™s
walking rate was 3 miles per hour and
Bobâ€™s was 4 miles per hour, how
many miles had Bob walked when
they met?

(A) 24
(B) 23
(C) 22
(D) 21
(E) 19.5

I believe that the answer that the official guide gives is not very precise...According to other books the process for solving questions like this is the following:

We add the rates of Yolanda and Bob--> 4+3=7
and then we divide this sum with the distance they have to cover in order to meet->
45/7= 6,43
this means that they have to walk for 6,43 hours (6 hours and (43x60)/100 minutes) in order to meet...

Bob, in 6 hours and 25,8 minutes can walk:

1 hour-->4miles
6h and 25,8 m-->25,032 miles

but this choice is not available at the OG...
The official answer is A and the explanation they give is the following:

Let t be the number of hours that Bob had
walked when he met Yolanda. Then,
when they met, Bob had walked 4t
miles and Yolanda had walked 3(t + 1)
miles. These distances must sum to 45
miles, so 4t + 3(t + 1) = 45, which
may be solved for t as follows. 4t + 3(t
+ 1) = 45, 4t + 3t + 3 =45, 7t = 42, so t
= 6 (hours). Therefore, Bob had
walked 4t = 4(6) = 24 miles when they
met. A is the correct answer.

Which one is the correct method? Which one should I use? I don't even understand why (in the OG) Yolanda had walked: 3(t+1) miles...

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1
KUDOS
Hi,

I hour after yolanda has started walking means Yolanda has covered 3 miles which means distance between bob and yolanda is 45-3 = 42 miles.

Relative velocity = 4+3 = 7 mph therefore they will take 42/7 = 6 hrs to meet at which me yolanda would have walked 3 x 6 = 18 miles and Bob would have walked 4*6= 24 . Therefore no ambiguity it A 24 miles

Hope this helps
_________________

Tony Chandra

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Location: Singapore
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Here's exactly how I would do it.

From X-Y, Yolanda covers 3 miles every hour. From Y-X, Bob covers 4 miles every hour. So for this 45 mile gap between them, every hour, 7 miles is trimmed off.

So it would take 45/7 = ~6 hours to meet. By this time, Bob must have walked 4*6 = 24 miles.
Intern
Joined: 20 Dec 2005
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tonychandra11 wrote:
Hi,

I hour after yolanda has started walking means Yolanda has covered 3 miles which means distance between bob and yolanda is 45-3 = 42 miles.

Relative velocity = 4+3 = 7 mph therefore they will take 42/7 = 6 hrs to meet at which me yolanda would have walked 3 x 6 = 18 miles and Bob would have walked 4*6= 24 . Therefore no ambiguity it A 24 miles

Hope this helps

I didn't notice that they didn't start walking at the same time...
Thank you very much!
Intern
Joined: 31 Dec 2005
Posts: 18
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Kudos [?]: 1 [0], given: 0

No problems . You are on your way
_________________

Tony Chandra

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