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

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VP
Joined: 21 Jul 2006
Posts: 1390
How much time did it take a certain car to travel 400 kilometers?  [#permalink]

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25 Jan 2008, 05:56
3
00:00

Difficulty:

35% (medium)

Question Stats:

68% (01:08) correct 32% (01:52) wrong based on 100 sessions

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

(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.

The OA is B. Can someone show how to solve this using the equation so that I can understand how option B is suff?
thanks

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CEO
Joined: 17 Nov 2007
Posts: 3423
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
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Re: How much time did it take a certain car to travel 400 kilometers?  [#permalink]

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25 Jan 2008, 06:16
$$(V+20)(t-1)=400$$

$$Vt=400$$

From second condition we can find t.
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Director
Joined: 12 Jul 2007
Posts: 838
Re: How much time did it take a certain car to travel 400 kilometers?  [#permalink]

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25 Jan 2008, 06:19
Distance: 400
Speed: x
Time: $formdata=\frac{400}{x}$

$formdata=\frac{400}{x}$ = $formdata=\frac{400}{x+20}$ + 1

Now solve:
$formdata=400(x+20)+=+400(x)+++x(x+20)$

$formdata=400x+8000+=+x^2+420x$

$formdata=x^2+20x-8000=0$

$formdata=(x+100)(x-80)=0$

so X is equal to 80 or -100. Obviously he can't be going -100km/h, so x = 80kmh.

Test it out:

$formdata=\frac{400}{80}=5$

and

$formdata=\frac{400}{100}=4$

Hope that helps
VP
Joined: 21 Jul 2006
Posts: 1390
Re: How much time did it take a certain car to travel 400 kilometers?  [#permalink]

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25 Jan 2008, 06:30
actually, where did you get this from:

400(x+20) = 400(x) + x(x+20)
Director
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Posts: 838
Re: How much time did it take a certain car to travel 400 kilometers?  [#permalink]

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25 Jan 2008, 07:24
tarek99 wrote:
actually, where did you get this from:

400(x+20) = 400(x) + x(x+20)

to eliminate the denominators I multiplied each term by x(x+20). Some of the terms canceled out, such as 400/x * x(x+20) where the x cancels out and we're left with 400(x+20)
Manager
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Re: How much time did it take a certain car to travel 400 kilometers?  [#permalink]

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06 May 2011, 09:30
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.
Director
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 03 Feb 2011
Posts: 725
Re: How much time did it take a certain car to travel 400 kilometers?  [#permalink]

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06 May 2011, 10:16
1) Insufficient
We dont know the average speed. Hence the time, spent in first 200 km does not make any sense.

2) Sufficient
vt = 400 -------(1)

vt = 200 = (v+ 20) (t - 1)

vt = vt + 20t - v - 20
20t = v + 20

Multiply both sides by t
20t^2 = vt + 20t
20t^2 = 400 + 20t -----(we know vt = 400)
t^2 = 20 + t

hence t^2 - t - 20 = 0

This will gives us two roots one positive and one negative. Hence t has unique value. Sufficient

hence B
naveenhv 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.
Director
Status: There is always something new !!
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Joined: 08 May 2009
Posts: 999
Re: How much time did it take a certain car to travel 400 kilometers?  [#permalink]

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06 May 2011, 10:22
let speed of the car = s
new speed = s+20

400/s - 400/(s+20) = 1
one known and one equation. It can be solved.

Hence B.

a. nothing provided for the rest half of the journey. not sufficient.
Director
Joined: 01 Feb 2011
Posts: 654
Re: How much time did it take a certain car to travel 400 kilometers?  [#permalink]

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06 May 2011, 10:25

Posted from my mobile device
Director
Joined: 01 Feb 2011
Posts: 654
Re: How much time did it take a certain car to travel 400 kilometers?  [#permalink]

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06 May 2011, 10:29
1
v = 400/t

1. Not sufficient

As we don't know about next 200km

2. Sufficient

v+20 =400/(t-1)
=> 400/t + 20 = 400/(t-1)
=> sufficient to find t

Posted from my mobile device
Math Expert
Joined: 02 Sep 2009
Posts: 52906
Re: How much time did it take a certain car to travel 400 kilometers?  [#permalink]

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28 Nov 2017, 22:26
How much time did it take a certain car to travel 400 kilometres?

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.

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Re: How much time did it take a certain car to travel 400 kilometers?   [#permalink] 28 Nov 2017, 22:26
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