Viper83 wrote:During a 40-mile trip, Marla traveled at an average speed of x miles per hour for the first y miles of the trip and at an average speed of 1.25x miles per hour for last 40-y miles of the trip. The time Marla took to travel the 40 miles was what percent of the time it would have taken her if she had traveled at an average speed of x miles per hour for the entire trip?

1. x=48
2. y=20

Time would have taken if speed was x mph, T = 40/x hour
Time taken in current situation, t = [(y/x) + (40 - y)/(5x/4)] hour
= [(y/x) + 4*(40 - y)/(5x)] hour
= [(5y + 160 - 4y)/(5x)] hour
= [(y + 160)/(5x)] hour

Required percentage = 100*(t/T) = 100*[(y + 160)/(5x)]/(40/x )
= 100*[(y + 160)/200] = (y + 160)/2

Thus the percentage depends upon y not on x.

Hence statement 1 is not sufficient whereas statement 2 is sufficient.

The correct answer is B.

Viper83 wrote:During a 40-mile trip, Marla traveled at an average speed of x miles per hour and for the first y miles of the trip and at an average speed of 1.25x miles per hour for last 40-y miles of the trip. The time Marla took to travel the 40 miles was what percent of of the time it would have taken her if she had traveled at an average speed of x miles per hour for the entire trip?

1. x=48
2. y=20

We are given that during a 40-mile trip, Marla traveled at an average speed of x miles per hour for the first y miles of the trip and at an average speed of 1.25x miles per hour for the last 40 - y miles of the trip. We are asked to determine what percentage the travel time for the 40-mile trip was of the time it would have taken her, had she traveled the entire trip at an average speed of x miles per hour.

Since time = distance/rate, the time it would have taken her to travel the entire trip at an average speed of x miles per hour is 40/x, and the actual time it took her to travel the entire trip at an average speed of x miles per hour for the first y miles of the trip and at an average speed of 1.25x miles per hour for the last 40 - y miles of the trip is y/x + (40 - y)/(1.25x). So the question becomes:

y/x + (40 - y)/(1.25x) is what percent of 40/x ?

[y/x + (40 - y)/(1.25x)]/(40/x) * 100 = ?

[y/x + (40 - y)/(1.25x)]/(40/x) * 100 = ?

[y/x + (40 - y)/(1.25x)] * (x/40) * 100 = ?

[y/40 + (40 - y)/50] * 100 = ?

2.5y + 2(40 - y) = ?

Thus, knowing the value of y will allow us to determine the above percentage.

Statement One Alone:
x = 48

Since we do not have any information about y, statement one alone is not sufficient. We can eliminate answer choices A and D.

Statement Two Alone:
y = 20

Since we have a value for y, statement two alone is sufficient. For practice, we can calculate the percentage as follows:

2.5(20) + 2(40 - 20) = 50 + 40 = 90

Answer: B

Here is a much easier way to look at it:

We already have a proportional difference in our rates: from x to 1.25x. If the distances were the same, we would already know the proportional difference (the percent change) in the times. Or if we knew the proportional difference in the distances, we'd be able to find the proportional difference in the times.

Target question: what is the ratio of the distances?
i.e. what is the value of y? If we know that, we'll know 40 - y.

Statement 1 gives us a value for the rate. This was irrelevant, since we already had a proportion between the rates.

Statement 2 gives us a value for the distance, so we can easily find the proportion between the two distances. In this case, the distances were the same, but it wouldn't have mattered. Any value for y is enough to give us the proportion or y to 40-y, so it would be sufficient.

The answer is B.