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]

06 Sep 2010, 12:09

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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.

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Re: Difficult DS Problem- Need Help! [#permalink]

06 Sep 2010, 12:41

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jjewkes wrote:

Can you help me with this problem??

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

(1) The car traveled the first 200 km in 2.5 hours.

(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.

I know that statement 2 is sufficient, but I cannot figure out why. I am getting a difficult quadratic equation when I try to put it into formulas. Obviously statement 1 is insufficient. Please help me understand this logic/algebra. Thanks!

Jeremiah

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.

Answer: B.

Hope it helps.
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Re: Difficult DS Problem- Need Help! [#permalink]

07 Sep 2010, 02:51

Agree ..I get +5 and -4 on solving the quadratic equation...so B is sufficient
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Re: Difficult DS Problem- Need Help! [#permalink]

07 Sep 2010, 22:11

It can be solved in an easier way.

Say it traveled initially with 80km per hour. So it covered 400 km in 5 hours.
Now adding 20km per hour . i.e 100 km per hour, it would have covered 400 km in 4 hours . Which is 1 hour less as per statement 2.

Makes life easy when u plugin numbers.

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Re: Difficult DS Problem- Need Help! [#permalink]

08 Sep 2010, 10:09

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anticipation wrote:

totally agree. while algebra is nice sometimes number plugin is easier to understand
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Re: Difficult DS Problem- Need Help! [#permalink]

20 Oct 2010, 06:46

Do we always have to solve the quadratic in such cases? You have 1 equation and you will obviously get 1 right answer as these are real speeds and we know for sure a solution exists. Given that this is a DS problem, is it safe to arrive at the equation and move on?

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Re: Data Sufficiency - Rate & Time problem [#permalink]

03 Dec 2010, 19:02

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Yellow22 wrote:

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

1) The car travelled the first 200 KM in 2.5 hrs?
2) If the Car's average speed was 20 KM per hour greater than it was, it would have travelled the 400 KM in 1 hour less time than it did.

I guess the solution is already clear to you.

Just for intellectual purposes, look at an alternative method:

If the car actually took t hours to cover 400 km, in the last 1 hour, the car travels a distance which is equal to 20*(t - 1) km
This must be the distance it covered in each hour since we are considering average speed.
400 = 20*(t - 1)*t
t(t - 1) = 20
t = 5 hrs
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Re: Data Sufficiency - Rate & Time problem [#permalink]

19 Jun 2011, 07:40

VeritasPrepKarishma wrote:

Yellow22 wrote:

Nice one. Could't understand completely at first glance until I broke the equation down :

( Let original Avg Speed = X km/hr, Time taken = t hr., Distance = 400 km)

From statement 2,

=> (X+20) km/hr * (t-1) hr = 400 km
=> [ X km/hr * (t-1)hr ]+ [20 km/hr * (t-1)hr] = 400 km
=> [ X km/hr * (t-1)hr ]+ [20 *(t-1) km/hr * 1hr] = 400 km ---> Equation (1)

From the original problem statement, the car travels 400 km at X km/hr in t hrs

So if the car travels at X km/ hr , the distance covered in the first (t-1hrs) is given by [ X km/hr * (t-1)hr ]
and the distance covered in the last 1 hr is given by [20 *(t-1) km/hr * 1hr]

Hence speed in the last 1 hr = [20 *(t-1)] km/hr ( and this would be the avg speed for the entire distance of 400km)

[20 *(t-1)] km/hr * t hr = 400 km

Upon solving we get t= 5hrs.

Thanks Karishma.

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

19 Jun 2012, 02:31

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

19 Jun 2012, 02:35

Stiv wrote:

Merging similar topics. Please ask if anything remains unclear.
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Re: How much time did it take a certain car to travel 400 km? [#permalink] 19 Jun 2012, 02:35

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