Speed Distance

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siddharth11.sharma@gmail.: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Wed Dec 05, 2012 8:02 am

Speed Distance

by siddharth11.sharma@gmail. » Mon Jul 22, 2013 1:34 pm

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 cars average speed had been 20 km/hr greater then it was, it would have travel led the 400 kilometers in 1 hr less time then it did.

On solving this one wud be geting a quadratic which gives you two values. Just skeptical about my approach, is there any other approach which i may be missing.

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Source: Beat The GMAT — Data Sufficiency | Mon Jul 22, 2013 1:34 pm

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by [email protected] » Mon Jul 22, 2013 1:38 pm

Hi siddharth11.sharma,

This DS question involves the Distance Formula ( D = R x T ). We're told that the Distance = 400km and asks about the Time.

Fact 1 doesn't give us enough info about the 400km trip, so...

Fact 1 is INSUFFICIENT

Fact 2 gives us this info:

400 = (R + 20)(T - 1)

From the prompt, we also have:

400 = (R)(T)

We have a "system" of equations, which we could solve and figure out the value of T.

Fact 2 is SUFFICIENT.

Final Answer: B

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Rich

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by Brent@GMATPrepNow » Mon Jul 22, 2013 2:20 pm

siddharth11.sharma@gmail. wrote: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 cars average speed had been 20 km/hr greater then it was, it would have travel led the 400 kilometers in 1 hr less time then it did.

Here's another approach:

Target question: How long did it take to travel 400km

To find the travel time, we need to know the average speed traveled.
Let x = the average speed traveled.

Rephrased target question: What is the value of x?

Statement 1: The car travelled the first 200km in 2.5hrs
No info about the 2nd half of the trip, so we can't determine the overall average speed.
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: If the car's average speed had been 20 km/h faster, it would have travelled the 400km in 1 hour less time.
Let's start with a word equation:
(travel time at x km/h) - 1 = (travel time at x+20 km/h)
Since time = distance/speed, we can now write:
(400/x) - 1 = 400/(x+20)

IMPORTANT: At this point, we need only determine whether or not this equation will yield 1 or 2 valid values of x. If it yields only 1 valid value, then statement 2 is sufficient. If it yields 2 valid values, then statement 2 is not sufficient.

Rewrite as: (400-x)/x = 400/(x+20)
Cross multiply: (400)(x) = (400-x)(x+20)
Simplify: 400x = 8000 + 380x - x^2
Rewrite: x^2 + 20x - 8000 = 0
Factor: (x + 100)(x - 80) = 0
So, x = -100 or 80
Since x cannot be negative, it must be the case that x = 80
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

by GMATGuruNY » Mon Jul 22, 2013 5:54 pm

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.

Statement 1: The car traveled the first 200 kilometers in 2.5 hours.
No information about the last 200 kilometers.
INSUFFICIENT.

Statement 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.
Since one speed is 20 kilometers greater than the other, the two speeds are likely to be factors of 400 that are 20 apart: 80 and 100.
Time to travel 400 kilometers at a speed of 80 miles per hour = 400/80 = 5.
Time to travel 400 kilometers at a speed of 100 miles per hour = 400/100 = 4 hours.
Time difference = 5-4 = 1 hour. Success!
No other combination of speeds will work.
To illustrate, if the speeds are 5 and 25, the difference in time = 400/5 - 400/25 = 80-16 = 64 hours.
Thus, the only speed that satisfies statement 2 is 80 kilometers per hour.
SUFFICIENT.

The correct answer is B.

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by Jeff@TargetTestPrep » Mon Dec 11, 2017 11:34 am

siddharth11.sharma@gmail. wrote: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 cars average speed had been 20 km/hr greater then it was, it would have travel led the 400 kilometers in 1 hr less time then it did.

We need to determine how much time it took a car to travel 400 kilometers.

Statement One Alone:

The car traveled the first 200 kilometers in 2.5 hours.

Since we don't know the time it takes to travel the final 200 kilometers, statement one is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

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.

Using the information in statement two, we can set up the following:

r = the average speed of the car

r + 20 = the average speed of the car when traveling 20 kilometers greater than it did

distance traveled = 400 kilometers

Since time = distance/rate, we can express time as the following:

time at normal rate = 400/r

time at faster rate = 400/(r+20)

Since when the car travels at the faster rate, the time is one hour less than when it travels at the normal rate, we can create the following equation:

400/r - 1 = 400/(r+20)

Multiplying the entire equation by r(r+20) gives us:

400(r+20) - r(r+20) = 400r

400r + 8000 - r^2 - 20r = 400r

r^2 + 20r - 8000 = 0

(r + 100)(r - 80) = 0

r = -100 or r = 80

Since we cannot have a negative rate, r = 80 km/hr. So the time it takes the car to travel 400 km is (400 km)/(80 km/hr) = 5 hours. Statement two is sufficient to answer the question.

Answer: B

Jeffrey Miller
Head of GMAT Instruction
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