Bunuel
On a recent trip, Mary drove 50 miles. What was the average speed at which she drove the 50 miles?
(1) She drove 30 miles at an average speed of 60 miles per hour and then drove the remaining 20 miles at an average speed of 50 miles per hour.
(2) She drove a total of 54 minutes.
We are being tested on average speed. The formula for average speed is:
average speed = total distance/total time
We are given that the total distance is 50 miles, so we can substitute 50 miles into our formula.
average speed = 50/total time
Thus, if we can determine the total time, we can determine the average speed.
Statement One Alone:She drove 30 miles at an average speed of 60 miles per hour and then drove the remaining 20 miles at an average speed of 50 miles per hour.
We are given that Mary first drove 30 miles at an average speed of 60 mph.
Since time = distance/rate, we can say:
time for the first 30 miles = 30/60 = ½ hour
We are also given that Mary drove the remaining 20 miles at an average speed of 50 miles per hour. Thus, we can say:
time for the remaining 20 miles = 20/50 = 2/5 hours
So we know that total time = ½ + 2/5 = 5/10 + 4/10 = 9/10 hours. Since we have the total time, we can determine average speed. Statement one is sufficient to answer question. We can eliminate answer choices B, C, and E.
Statement Two Alone:She drove a total of 54 minutes.
We are given the total time, so statement two is also sufficient to answer the question.
The answer is D.