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Prompt: How long did it take Betty to drive nonstop on a trip from her home to Denver, Colorado?

To apply D = RT, we would have to know both the distance and the speed to find the time.

Statement #1: If Betty's average speed for the trip had been 1 and 1/2 times as fast, the trip would have taken 2 hours.

Let D be the distance, and R be her speed. What this is saying is:

D = (1.5R)*2 = 3*R

This implies T = D/R = 3 --- the trip took her 3 hours. Statement #1, by itself, is sufficient.

Statement #2: Betty's average speed for the trip was 50 miles per hour.

Well, we know the average speed, but we don't know where Betty lives --- we have no idea of the distance from her home to Denver. Since we know R and don't know D, we can't find T. Statement #2, by itself, is insufficient.

Here's a similar DS question, for more practice: http://gmat.magoosh.com/questions/927 When you submit your answer to that, the next page will have a complete video explanation.

Does all this make sense? Please let me know if you have any questions.

Prompt: How long did it take Betty to drive nonstop on a trip from her home to Denver, Colorado?

To apply D = RT, we would have to know both the distance and the speed to find the time.

Statement #1: If Betty's average speed for the trip had been 1 and 1/2 times as fast, the trip would have taken 2 hours.

Let D be the distance, and R be her speed. What this is saying is:

D = (1.5R)*2 = 3*R

This implies T = D/R = 3 --- the trip took her 3 hours. Statement #1, by itself, is sufficient.

Statement #2: Betty's average speed for the trip was 50 miles per hour.

Well, we know the average speed, but we don't know where Betty lives --- we have no idea of the distance from her home to Denver. Since we know R and don't know D, we can't find T. Statement #2, by itself, is insufficient.

Here's a similar DS question, for more practice: http://gmat.magoosh.com/questions/927 When you submit your answer to that, the next page will have a complete video explanation.

Does all this make sense? Please let me know if you have any questions.

Mike

D = (1.5R)*2 = 3*R

Hi, Should the above not be D = (2.5R)*2 = 3*R?

doesnt '1.5 times as fast ' imply 2.5R?
_________________

hope is a good thing, maybe the best of things. And no good thing ever dies.

If I have a speed that is 1.5 times faster than this, that's 2.5*V If I have a speed that is 1.5 times as fast as this, that's 1.5*V Is my understanding correct?

Dear Sachin

We are getting into some really subtleties of grammar and phrasing here.

If I have a speed that is 1.5 times as fast as V ----> that clearly should be 1.5*V

If my speed was V, but increased by 1.5 this value ----> that clearly should be 2.5*V

If I have a speed that is 1.5 times faster than V -----> not 100% percent clear, but I would say most people would interpret this as 1.5*V. The GMAT is always crystal clear in its phrasing. There is no way they would use this phrasing and expect you to come up with 2.5*V.

Part of what is unusual about this conversation is we are talking about the increases of speed. Almost everyone compares speed by saying "n times faster." In real life, no one ever talks about percentage increase or decreases for speed.

Let's change the subject to something like profits. You are perfectly correct ---- If I say "profits increased by 150%", that's 2.5 times the original profits.

If I have a speed that is 1.5 times faster than this, that's 2.5*V If I have a speed that is 1.5 times as fast as this, that's 1.5*V Is my understanding correct?

Dear Sachin

We are getting into some really subtleties of grammar and phrasing here.

If I have a speed that is 1.5 times as fast as V ----> that clearly should be 1.5*V

If my speed was V, but increased by 1.5 this value ----> that clearly should be 2.5*V

If I have a speed that is 1.5 times faster than V -----> not 100% percent clear, but I would say most people would interpret this as 1.5*V. The GMAT is always crystal clear in its phrasing. There is no way they would use this phrasing and expect you to come up with 2.5*V.

Part of what is unusual about this conversation is we are talking about the increases of speed. Almost everyone compares speed by saying "n times faster." In real life, no one ever talks about percentage increase or decreases for speed.

Let's change the subject to something like profits. You are perfectly correct ---- If I say "profits increased by 150%", that's 2.5 times the original profits.

Does all this make sense?

Mike

You Mike, It does Thanks a lot
_________________

hope is a good thing, maybe the best of things. And no good thing ever dies.

How long did it take betty to drive nonstop on a trip from her home to Denver, Colorado?

(1). If Betty's average speed for the trip had been 1 1/2 times as fast, the trip would have taken 2 hours.

(2). Betty's average speed for the trip was 50 miles / hour.

The distance is similar in this question

equation 1 X be speed, t is the time and d is the distance

X*t=d

equation 2

1.5X*2=d >> 3X=d

substitute in 1

x*t=3X

t=3

is this approach correct?

Yes, it is. Even without any formula: since moving 1.5 times as fast as the actual speed would take 2 hours to cover the distance, then moving at actual speed would take 2*1.5=3 hours to cover the same distance.
_________________

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