Rate - How long did it take

[DCJ]

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 per hour

[truplayer256]

Statement 1: The total distance from Betty's home to Denver, Colorado=y miles.

The total amount of time it took Betty to travel those y miles= t hours.

y/2=3/2(y/t)

y/3=y/t

yt=3y

t=3 hours

SUFFICIENT.

Statement 2: total distance/total time= average speed. Only the average speed is given to us which leads us to 2 unknowns. INSUFFICIENT.

A

[vinayakdl]

One more for A.

Vinayak

[Brent@GMATPrepNow]

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 per hour

Target question: What was Betty's travel time?

Let D = The distance driven
Let R = Betty's average speed

Since Time = Distance/Rate, we can re[phrase the target question. . .

Rephrased target question: What is the value of D/R?

Statement 1: If Betty's avg speed for the trip had been 1.5 times as fast, the trip would have taken 2 hours.
The distance is still the same (D), but the rate is 1.5R
So, statement 1 tells us that D/1.5R = 2
Is this enough information to find the value of D/R?
Sure, just take the equation D/1.5R = 2 and multiply both sides by 1.5 to get D/R = 3
Since we're able to answer the rephrased target question with certainty, statement 1 is SUFFICIENT

Statement 2: Betty's avg speed for the trip was 50 miles per hour.
This tells us that R=50
However, we cannot find the value of D/R, since we don't know the value of D (distance)
So, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent