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

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How much time did it take a certain car to travel 400 kilometers? [#permalink]

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29 Nov 2007, 01:13
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Difficulty:

35% (medium)

Question Stats:

73% (01:42) correct 27% (01:23) wrong based on 141 sessions

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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 hour less time than it did.

OPEN DISCUSSION OF THIS QUESTION IS HERE: how-much-time-did-it-take-a-certain-car-to-travel-100514.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 16 Feb 2015, 04:16, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: How much time did it take a certain car to travel 400 kilometers? [#permalink]

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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: How much time did it take a certain car to travel 400 kilometers? [#permalink]

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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

Note: I sometimes feel i can resolve the problems easily..but when i take a prep-test...i would fail to solve even the simplest...so its pressure which is reducing my efficiency... does anybody else too are facing this?
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Re: How much time did it take a certain car to travel 400 kilometers? [#permalink]

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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: How much time did it take a certain car to travel 400 kilometers? [#permalink]

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26 Jun 2011, 20:34

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: How much time did it take a certain car to travel 400 kilometers? [#permalink]

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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: How much time did it take a certain car to travel 400 kilometers? [#permalink]

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27 Jun 2011, 03:05
B

Posted from my mobile device
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Re: How much time did it take a certain car to travel 400 kilometers? [#permalink]

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27 Jun 2011, 04:48
[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: How much time did it take a certain car to travel 400 kilometers? [#permalink]

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27 Jun 2011, 21:35
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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

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Re: How much time did it take a certain car to travel 400 kilometers? [#permalink]

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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: How much time did it take a certain car to travel 400 kilometers? [#permalink]

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Re: How much time did it take a certain car to travel 400 kilometers? [#permalink]

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16 Feb 2015, 04:17
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Expert's post
mexicanhoney wrote:
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 hour less time than it did.

Let the average speed of the car be $$s$$ km/h and the time it spent to cover 400 km be $$t$$ hours, then $$st=400$$ ($$s=\frac{400}{t}$$). Question: $$t=?$$

(1) The car traveled the first 200 km in 2.5 hours --> we don't know the time the car needed to travel the second 200 km, so this statement is clearly insufficient.

(2) If the car's average speed had been 20km per hour greater than it was, it would have traveled the 400km in 1 hour less than it did --> $$(s+20)(t-1)=400$$ --> $$st-s+20t-20=400$$ --> as $$st=400$$ and $$s=\frac{400}{t}$$ --> $$400-\frac{400}{t}+20t-20=400$$ --> 400 cancels out and after simplification we'll get: $$20t^2-20t-400=0$$ --> $$t^2-t-20=0$$ --> $$(t-5)(t+4)=0$$ --> $$t=5$$ or $$t=-4$$ (not a valid solution as time can not be negative), so $$t=5$$. Sufficient.

OPEN DISCUSSION OF THIS QUESTION IS HERE: how-much-time-did-it-take-a-certain-car-to-travel-100514.html
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Re: How much time did it take a certain car to travel 400 kilometers?   [#permalink] 16 Feb 2015, 04:17
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