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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]

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25 Jan 2008, 06:56
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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.

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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25 Jan 2008, 07:16
$$(V+20)(t-1)=400$$

$$Vt=400$$

From second condition we can find t.
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25 Jan 2008, 07:19
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
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25 Jan 2008, 07:30
actually, where did you get this from:

400(x+20) = 400(x) + x(x+20)
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25 Jan 2008, 08:24
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)
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06 May 2011, 10:30
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.
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06 May 2011, 11:16
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.
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06 May 2011, 11:22
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.
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06 May 2011, 11:25

Posted from my mobile device
Director
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06 May 2011, 11:29
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
Re: Rates   [#permalink] 06 May 2011, 11:29
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