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How much time did it take a certain car to travel 400

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How much time did it take a certain car to travel 400 [#permalink] New post 13 Nov 2011, 01:19
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A
B
C
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E

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Question Stats:

86% (02:07) correct 14% (00:00) wrong based on 7 sessions
How much time did it take a certain car to travel 400 kilometers?
(1) The car traveled the first 200 kilometers in 2.5 hours
(2) If the car's average speed had been 20 kilometers per hour greater than it was, it would have traveled the 400 kilometers in 1 hours less time than it did.

Statement 1 - I understand not sufficient.

But how come statement 2 be Sufficient?
[Reveal] Spoiler: OA

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Re: Car and 400 Kms Distance - Ivy 26 [#permalink] New post 13 Nov 2011, 02:10
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Hey..

The answer is B.

It is given that the distance to be covered is 400kms in the question. Taking speed as s km/hr and time as t hrs, we have the eqn

400 = st ----> (1)

In B, it i given as the same distance would be covered by less than an hour if the car had traveled in a speed greater than 20km/hr that it was.

so this can be equated as,

400 = (s+20)(t-1) ---> (2)

Equating (1) and (2) we have,

st = (s+20)(t-1)
st = st + 20t - s - 20
0 = 20t - s - 20

Again substitute the value of s from eqn (1)
0 = 20t - 400/t - 20
divide it by 20
0 = t -20/t - 1

Multiply by t throughout,
0 = t^2 - 20 - t
so,

t^2 - t - 20 = 0
Solving for t, we get
t=5 , -4
T=-4 is not possible,
hence t = 5 hrs

Hope it helps.
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Re: Car and 400 Kms Distance - Ivy 26 [#permalink] New post 13 Nov 2011, 02:21
The only information given in the question is that the total distance travelled by the car is 400kms. We have to find the time taken by the car to do so.

Now, let's take a look at the given options.

Statement 1 says that the car traveled the first 200 kilometers in 2.5 hours. This does not give us any information about the remaining 200 km that the car travelled.
Hence this is clearly Insufficient.

Statement 2 says that If the car's average speed had been 20 kilometers per hour greater than it was, it would have traveled the 400 kilometers in 1 hours less time than it did. This seems to be quite a lengthy statement, so let's break this down into simpler sentences to make the given information clear.

Let's assume that the car's average speed for the 400 km travel was 'x' km per hour.
Also, let the time taken to travel be 't' hours.
So, we have t = 400/x -----> (A)

Statement 2 says that if the car's average speed had been 20 km per hour greater than it was (earlier). This indicates that the new speed is 'x+20' km per hour
The car would have travelled 400 km in 1 hour less time than it did (earlier). This indicates that the time taken later (in the new scenario) is 't-1' hours
We know that the car still travelled 400 km, so the new equation can be written as
t-1 = 400/(x+20) -----> (B)

But we know from 'A' that t = 400/x
Substituting this value in the equation 'B', we get

400/x - 1 = 400/(x+20)
Simplifying, we get,
400x = 400x - x^2 + 8000 -20x
i.e. x^2 + 20x - 8000 = 0

Solving the above quadratic equation yields the solutions x = 80 OR x = -100
As the speed of the car cannot be negative, the required speed is 80 km per hour

Using this, we can determine the time taken by the car to travel 400 km. This comes to 5 hours.
Hence Statement 2 alone is sufficient to answer the question.

Hope this helps. :)

Cheers!
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Re: Car and 400 Kms Distance - Ivy 26 [#permalink] New post 13 Nov 2011, 02:30
Using statement 2, if v is the speed of the car then:
400/v = 400/(v+20) + 1

Solve this to get v and then compute 400/v. Sufficient. So (B).
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Director
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Status: Preparing for the 4th time -:(
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Re: How much time did it take a certain car to travel 400 [#permalink] New post 14 Nov 2011, 06:17
Too good explanation esp. You are a star. Many thanks buddy. :lol:
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Re: How much time did it take a certain car to travel 400   [#permalink] 14 Nov 2011, 06:17
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