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# Bob and Wendy left home to walk together to a restaurant

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Bob and Wendy left home to walk together to a restaurant [#permalink]

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10 Jul 2007, 10:44
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Hi all,

Looking for help on a Manhattan GMAT question.

Bob and Wendy left home to walk together to a restaurant for dinner. They started out walking at a constant pace of 3 mph. At precisely the halfway point, Bob realized he had forgotten to lock the front door of their home. Wendy continued on to the restaurant at the same constant pace. Meanwhile, Bob, traveling at a new constant speed on the same route, returned home to lock the door and then went to the restaurant to join Wendy. How long did Wendy have to wait for Bob at the restaurant?

(1) Bob’s average speed for the entire journey was 4 mph.

(2) On his journey, Bob spent 32 more minutes alone than he did walking with Wendy.

The answer, that (2) alone is sufficient, doesn't really make sense to me. Manhattan has an explanation but I was wondering if someone could help me to understand this better. Thanks!
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10 Jul 2007, 10:58
I think the answer for this is C

With Stmt 1 we get Bob's speed alone at 4.5mph
With Stmt 2 we get the ratio of distance to bob speed alone.

Combining we get the time Wndy spent. I am surprised that we could solve it with Stmt 2.

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10 Jul 2007, 11:17
This question cannot necessarily be rephrased, but it is important to recognize that we need not necessarily calculate Wendy’s or Bob’s travel time individually. Determining the difference between Wendy’s and Bob’s total travel times would be sufficient. This difference might be expressed as tb – tw.

(1) INSUFFICIENT: Calculating Bob’s rate of speed for any leg of the trip will not give us sufficient information to determine the time or distance of his journey, at least one of which would be necessary to determine how quickly Wendy reaches the restaurant.

(2) SUFFICIENT: To see why this statement is sufficient, it is helpful to think of Bob's journey in two legs: the first leg walking together with Wendy (t1), and the second walking alone (t2). Bob's total travel time tb = t1 + t2. Because Wendy traveled halfway to the restaurant with Bob, her total travel time tw = 2t1. Substituting these expressions for tb – tw,

t1 + t2 – 2t1 = t2 – t1

tb – tw = t2 – t1

Statement (2) tells us that Bob spent 32 more minutes traveling alone than with Wendy. In other words, t2 – t1 = 32. Wendy waited at the restaurant for 32 minutes for Bob to arrive.

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10 Jul 2007, 22:00
The lucky thing is that it is a DS question...we only need to determine that we have sufficient information.

If bob spent 32 minutes more alone than he did with wendy, she had to wait for him for 32 minutes... She had already traveled half way which means that it would take the same amount of time to reach the resturaunt. Bob got there 32 minutes after that time
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11 Jul 2007, 12:57
the question is poorly worded..time spent alone doesnt equal to time wendy spent alone at the resturant...
11 Jul 2007, 12:57
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