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M16#8

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M16#8 [#permalink] New post 04 Feb 2009, 06:48
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If it took a bus 4 hours to get from town A to town B, what was the average speed of the bus for the trip?

(1) In the first 2 hours the bus covered 100 miles.
(2) The average speed of the bus for the first half of the distance was twice its average speed for the second half.

[Reveal] Spoiler: OA
E

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Re: M16#8 [#permalink] New post 05 Feb 2009, 07:06
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scthakur wrote:
E is right. It is required to know the average speed of the first half or of second half of distance. Stmt1 does not help obtain this. Stmt1 simply tells that the bus travelled a distance of 100 miles in two hours.


I think scthakur got it that I missed.

Statement 1 talks about the first two hours.
Statement 2 talkes about the average speeds of the bus for the first half and second half of the distance.

St1 and 2 are talking entirely two different things. so Agree with E.

topmbaseeker wrote:
It took the bus 4 hours to get from town A to town B. What was the average speed of the bus for the trip?

1. In the first 2 hours the bus covered 100 miles
2. The average speed of the bus for the first half of the distance was twice its speed for the second half

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Re: M16#8 [#permalink] New post 05 Feb 2009, 03:21
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E is right. It is required to know the average speed of the first half or of second half of distance. Stmt1 does not help obtain this. Stmt1 simply tells that the bus travelled a distance of 100 miles in two hours.
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Re: M16#8 [#permalink] New post 27 Jan 2010, 08:04
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We need to know the total distance to come up with the average speed.

S1 - In the first 2 hours the bus covered 100 miles - not suff as it just talks about the 1st 2 hrs and the distance travelled. In next 2 hrs distance can be 100,200,150 or anything.
S2 - The average speed of the bus for the first half of the distance was twice its speed for the second half - not sufficient .....talks about the speed was twice but still doesnt tell what the distance of the 1st half was.

Together - S2 talks about the av. speed for the 1st half of the distance but doesnt say that 1st half is 100 miles. So we cant use statement 1 to come up with the total distance.

Hence answer E.
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Re: M16#8 [#permalink] New post 04 Feb 2009, 06:50
Can't the first two hours i.e. 100 miles be the first part of the distance which can be used along with (2) to find the average speed? I am surprised at the official answer.
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Re: M16#8 [#permalink] New post 04 Feb 2009, 07:37
topmbaseeker wrote:
It took the bus 4 hours to get from town A to town B. What was the average speed of the bus for the trip?

1. In the first 2 hours the bus covered 100 miles
2. The average speed of the bus for the first half of the distance was twice its speed for the second half

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1: what about the second 2 hours? nsf.
2: ok, avg. speed for the first half (i.e. half of the total distance) was twice the speed for the second half. but what is the spped? nsf..


togather: first half speed = 100 miles/2 hrs = 100 mph.
second half speed = 200 mph (from st. 2)

so total distance = distance in first 2 hours + distance in second 2 hours = 200+400 = 600 miles

avg. speed = 600/4 = 150 mph

So C.
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Re: M16#8 [#permalink] New post 04 Feb 2009, 07:39
topmbaseeker wrote:
Can't the first two hours i.e. 100 miles be the first part of the distance which can be used along with (2) to find the average speed? I am surprised at the official answer.



Thats not correct. we do not know the speed of the bus for the second 2 hours. It could be 100mph or 200 mph or 300 mph.
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Re: M16#8 [#permalink] New post 04 Feb 2009, 20:53
But you have (1) which will give you the speed for the first 2 hours. I also choose C but the official answer is E.
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Re: M16#8 [#permalink] New post 04 Feb 2009, 21:07
topmbaseeker wrote:
But you have (1) which will give you the speed for the first 2 hours. I also choose C but the official answer is E.


I would like to know OE. Do not see any reason that E is the OA.
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Re: M16#8 [#permalink] New post 05 Feb 2009, 04:40
Why can't statement 1 give you average speed?
d = r t
100 = r * 2

therefore r = 50.

I still feel that the ans should be C
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Re: M16#8 [#permalink] New post 11 Feb 2009, 09:57
I choose C for this question.

As the distance from A to B is divided into two equal parts. So I call the speed and time to travel the 1st half of the road are S1, T1 respectively. The speed and time for second half are S2, T2. We have s1*t1 = s2*t2

We have these following equations:

T1+T2 = 4
S1= 2 S2 ( the second statement) => t2= 1/2 t1 (equal distances)

=> t1 = 4/3(h) t2 = 8/3(h)

Then use statement 1: 100 = 4/3*s1 + 2/3* s2 ( statement 1 : 100 miles for 2h)
s1= 2 s2
s1= 60 , s2 =30

=> AB = 160 (miles) => average speed = 40(mph)

Am I right???
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Re: M16#8 [#permalink] New post 27 Jan 2010, 10:20
It has to be E.

Statement 1 misses what is 100 miles.It can be half, 2/3rd or any part of the total distance. Hence, total distance is unknown.
Statement 2 misses to replace the variables of time, speed and distance in correct form.

Both statement lack the purpose due to the same logic as in statement 1.
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Re: M16#8 [#permalink] New post 27 Jan 2010, 23:08
This was a good practice problem. I struggled between C and E and can't really say that I chose either. C was the most bothersome though because on the surface it appears that you can obtain relevant numbers for the second part of the trip. However, since the rate and distance isn't explicit, one should call the statements as presented-insufficient.

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Re: M16#8 [#permalink] New post 28 Jan 2010, 10:43
topmbaseeker wrote:
It took the bus 4 hours to get from town A to town B. What was the average speed of the bus for the trip?

1. In the first 2 hours the bus covered 100 miles
2. The average speed of the bus for the first half of the distance was twice its speed for the second half

[Reveal] Spoiler: OA
E

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Very tricky wording. Notice that S2 says "the average speed of the bus for the first half of the distance was twice its speed for the second half. So just because S1 gives us the first half of the trip, we don't know the total distance so we don't know that the first half of the trip time-wise is the same as the first half of the trip distance-wise. Accordingly, we can't speak to the average speed or distance during the second two hours; E.
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Re: M16#8 [#permalink] New post 28 Jan 2010, 11:30
just to make it clearer, I'll point out the flaw in huuminh2211's equations.

he says:
"Then use statement 1: 100 = 4/3*s1 + 2/3* s2 ( statement 1 : 100 miles for 2h)
s1= 2 s2"

Although s2 is the "average" speed for the second half of the trip, it is not necessarily the average speed for any part of it. so using average speed for distance covered from time=4/3 hours till time=2 hours is not necessarily s2.
otherwise, huuminh2211's equations are all right.
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Re: M16#8 [#permalink] New post 28 Jan 2010, 12:16
1. 100 miles in 2 hrs does not give any more information about total distance -- Not Sufficient
2. avg speed of ( 1/2 distance) = 2 avg speed of (second half distance) -- Not Sufficient.
Together, we still don't know the total distance traveled in 4 hrs. so answer is E.
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Re: M16#8 [#permalink] New post 01 Feb 2010, 12:04
IMO its E

1. Its not sufficient as its just giving us information for the first 2 hours, with no information of the speed being constant or varying.

2. This is also not sufficient.

Take Avg speed = total dist/total time = \frac{2d}{t1+t2} ---1

T = t1+ t2 = \frac{d}{2x} + \frac{d}{x}
=> 4 =\frac{3d}{2x} ----2

from equation 1 and 2 we can conclude we dont have value of X.
Thus not sufficient and ans is E
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Re: M16#8 [#permalink] New post 17 Feb 2010, 09:14
gurpreetsingh wrote:
IMO its E

1. Its not sufficient as its just giving us information for the first 2 hours, with no information of the speed being constant or varying.

2. This is also not sufficient.

Take Avg speed = total dist/total time = \frac{2d}{t1+t2} ---1

T = t1+ t2 = \frac{d}{2x} + \frac{d}{x}
=> 4 =\frac{3d}{2x} ----2

from equation 1 and 2 we can conclude we dont have value of X.
Thus not sufficient and ans is E


hi gurpreet
can u pls explain how can u consider that in the second half he covered the same distance....i.e d....
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Re: M16#8 [#permalink] New post 17 Feb 2010, 10:56
topmbaseeker wrote:
It took the bus 4 hours to get from town A to town B. What was the average speed of the bus for the trip?

1. In the first 2 hours the bus covered 100 miles
2. The average speed of the bus for the first half of the distance was twice its speed for the second half

[Reveal] Spoiler: OA
E

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Shalu pls read the statement 2 again..

avg speed of 1st half = twice of second half..that means distance same taken for the calculation.
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Re: M16#8 [#permalink] New post 01 Mar 2010, 13:35
I strongly feel the distance in the first half and second half cannot be the same.
Eg:
We know the total time = 4 Hrs
Say Speed 1 = 100m/h , then as per Stmt 2, Speed 2 = 50 m/h
Time1 = 2 Hrs Time2 = 2 Hrs
Distance1 = 200Miles Distance2 = 100 Miles

So there is no way the distances can be equal.
Re: M16#8   [#permalink] 01 Mar 2010, 13:35
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