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

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How much time did it take a certain car to travel 400 km? [#permalink] New post 29 Nov 2007, 01:13
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40% (01:48) correct 60% (01:14) wrong based on 5 sessions
How much time did it take a certain car to travel 400 km?

(1) The car traveled the first 200 km in 2.5 hrs.
(2) If the car's average speed had been 20 km per hour greater than it was, it would have traveled the 400 km in 1 hour less time than it did.
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 [#permalink] New post 29 Nov 2007, 04:05
It looks like B

We can see that 80kph means the journey lasts 5 hours
Add 20kph and the journey lasts 4 hours.

I don't imagine there's another solution?
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Re: DS - time it took to travel [#permalink] New post 26 Jun 2011, 09:56
can this solution be discussed too?

from my analysis

1. This does not talk about the other 200kms at all, hence not giving any solutions

2.
with current speed, it can be written as
s=400/t
where s = current speed and t= current time

if speed is increased by 20, then s=s+20 and time reduces by 1 hr meaning t=t-1
but t=400/s from first equation
so now we have
s+20 = 400/(t-1)
substituting for t in above equation we get
s+20 = 400/((400/s) - 1)
s+20 = 400s/(400-s)
so since it is having a single variable to resolve and to find out the speed, we can then find out the time taken too...
hence possible.

so B

hope this answers....

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Re: DS - time it took to travel [#permalink] New post 26 Jun 2011, 20:04
harshavmrg,

I got to the level you discussed above, but Statement II leads to quadratic equation in t (time taken to travel) which may also lead to 2 solutions!

So I think the answer is E.
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Re: DS - time it took to travel [#permalink] New post 26 Jun 2011, 20:34
The answer would be B.

You would get a quadratic equation, however one of the roots would be negative and hence can be ruled out.
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Re: DS - time it took to travel [#permalink] New post 26 Jun 2011, 20:39
How can be so sure of signs? why can't they both be -ves or +ves
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Re: DS - time it took to travel [#permalink] New post 27 Jun 2011, 03:05
B

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Re: DS - time it took to travel [#permalink] New post 27 Jun 2011, 04:48
IMO answer is
[Reveal] Spoiler:
B


St1: insufficient - we dont know what the speed was for the other half of the journey
St 2: gives us a modification to the given statement --> (V+20)*(T-1)= 400 = VT. This results in the quadratic eq: t2-t-20=0. Now, since D = (b2-4ac) = 81 is > 0 therefore, there are two solutions:

t= [-(-1)+9]/2 = 5 and t = [-(-1)-9]/2 = -4 (negative sol. is not possible) so, t=5
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Re: DS - time it took to travel [#permalink] New post 27 Jun 2011, 21:35
1. Not sufficient.

we dont know whether car was travelling at uniform rate or not. We also dont know the rest of the journey speed.

2. Sufficient

20 + v = 400/(t-1)
20+(400/t) = 400/(t-1)

t =5

Answer is B.
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Re: DS - time it took to travel [#permalink] New post 30 Jun 2011, 07:47
because from the question, we know that there is some speed taken to cover a distance, hence that speed is greater than 0...

this is just my assumption...and the total time taken is lessened by just 1 hr....hence the speed would be greater than zero and as informed in the question that the new speed would be greater than the current speed.
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Re: DS - time it took to travel   [#permalink] 30 Jun 2011, 07:47
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