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# Bob and Wendy planned to walk from their home to a

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Joined: 08 Oct 2009
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Bob and Wendy planned to walk from their home to a  [#permalink]

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26 Jan 2010, 21:01
4
10
00:00

Difficulty:

45% (medium)

Question Stats:

72% (01:55) correct 28% (01:52) wrong based on 676 sessions

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Bob and Wendy planned to walk from their home to a restaurant for dinner together. However, Bob was delayed at work, and Wendy left for the restaurant before Bob did. If the restaurant is 3 miles from their home and Bob left for the restaurant a half-hour after Wendy did, how long did Wendy have to wait for Bob at the restaurant?

(1) Wendy walked at a constant pace of 4 miles per hour

(2) Bob walked at a constant pace of 1 mile per hour faster than Wendy.
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Re: MGMAT DS, Rates Need a better explanation  [#permalink]

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27 Jan 2010, 05:12
10
8
Bob and Wendy planned to walk from their home to a restaurant for dinner together. However, Bob was delayed at work, and Wendy left for the restaurant before Bob did. If the restaurant is 3 miles from their home and Bob left for the restaurant a half-hour after Wendy did, how long did Wendy have to wait for Bob at the restaurant?

(1) Wendy walked at a constant pace of 4 miles per hour

(2) Bob walked at a constant pace of 1 mile per hour faster than Wendy.

OA to Come

$$t=(\frac{3}{b}+\frac{1}{2})-\frac{3}{w}$$, where $$t$$ is the waiting time for Wendy, $$b$$ is the Bob's rate and $$w$$ is the Wendy's rate.

Hence we need both $$b$$ and $$w$$, to calculate $$t$$.

(1) Gives us $$w=4$$, $$b=?$$, not sufficient;
(2) Gives us the relationship between $$w$$ and $$b$$, $$w+1=b$$. Still insufficient, we should know the exact numerical value of at least one of them.

(1)+(2) From (1) we know $$w$$, hence from (2) we can get $$b$$. Sufficient.

Just to illustrate: $$t=(\frac{3}{b}+\frac{1}{2})-\frac{3}{w}=(\frac{3}{4+1}+\frac{1}{2})-\frac{3}{4}=\frac{7}{20}$$, $$21$$ min. Sufficient.

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Re: Bob and Wendy planned to walk from their home to a  [#permalink]

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30 Jul 2013, 14:33
1
Bob and Wendy planned to walk from their home to a restaurant for dinner together. However, Bob was delayed at work, and Wendy left for the restaurant before Bob did. If the restaurant is 3 miles from their home and Bob left for the restaurant a half-hour after Wendy did, how long did Wendy have to wait for Bob at the restaurant?

(1) Wendy walked at a constant pace of 4 miles per hour
Time = Distance/Rate
Time = 3/4
It took her 3/4ths of an hour (45 minutes) to get to the restaurant.

Still, we know nothing about about the rate at which Bob traveled after Wendy left.
INSUFFICIENT

(2) Bob walked at a constant pace of 1 mile per hour faster than Wendy.

We don't know Wendy's rate so we don't know Bob's either.
INSUFFICIENT

1+2)

Wendy rate = 4 miles/hour
Bob rate = 4+1 miles/hour

Time = Distance/Rate
Time = 3/5
It took him 3/5ths of an hour (36 minutes) to get to the restaurant.

She takes 45 minutes to get to the restaurant. Bob leaves when she is 15 minutes away. It takes him 36 minutes to get there from the point when she is 15 minutes away. In 15 minutes she is at the restaurant and bob is 36-15=21 minutes away.

She waits for 21 minutes.
SUFFICIENT

(C)
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Re: Bob and Wendy planned to walk from their home to a  [#permalink]

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29 Jan 2016, 06:43
I didnt understand why statement 1/2 alone arent sufficient. Please let me know where am I going wrong

Question interpretation:
Wendy reached in 't'
Since Bob started late half an hr therefore Bob must have reached in t+1/2

Statement 1:- Given Wendy's speed is 4

therefore we can calculate t since we know the distance = 3
Once we get t we can find time taken by Bob as well

Statement 2 : -
s= speed of Wendy
we know for Bob = (s+1) (t+1/2)=3
for Wendy = s(t )=3

If we equate both we can find t .

Where am I going wrong? Why cant we relate Bob & Wendy's time?
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Joined: 22 Mar 2011
Posts: 1564
Re: Bob and Wendy planned to walk from their home to a  [#permalink]

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30 Jan 2016, 01:01
1
Seemachandran, your solution requires us to assume that Bob takes the same amount of time to make the trip as Wendy. Without the statements, we know nothing about this. So he may arrive hours later or just a short time after Wendy--we have no idea. (Also, be careful with your equation: we don't want to multiply Bob's speed by (t+1/2), since he isn't walking during that half hour. His speed during that time is zero!)

Statement 1 tells us nothing about Bob, so there is no way to solve.

Statement 2 tells us that Bob is 1 mph faster than Wendy, but that's not sufficient. Here are a few possibilities:

Wendy's rate is 5 mph and Bob's is 6 mph. Her walk is 36 min and Bob's is 30 min. Since she left 30 min earlier, he arrives 24 minutes after her.
Wendy's rate is 4 mph and Bob's is 5 mph. Her walk is 45 min and Bob's is 36 min. Since she left 30 min earlier, he arrives 21 minutes after her.

More than one possibility? This is insufficient, but if we combine 1&2 we get the second possibility above. Sufficient!
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Re: Bob and Wendy planned to walk from their home to a  [#permalink]

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01 Nov 2018, 08:47
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Re: Bob and Wendy planned to walk from their home to a   [#permalink] 01 Nov 2018, 08:47
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