On a certain nonstop trip, Marta…
We are given that Marta averaged x miles per hour for 2 hours and y miles per hour for the remaining 3 hours. Since distance = rate x time, Marta drove 2x miles for the first two hours and 3y miles for the remaining 3 hours. We must determine the average rate. The equation for average rate is:
average rate = total distance/total time
Thus, Marta’s average speed, in miles per hour, is:
(2x + 3y)/5
If we can determine the value of 2x + 3y, we can determine Marta’s average speed for the entire trip.
Statement One Alone:
2x + 3y = 280
Since we have the value of 2x + 3y, we can determine the average speed for the entire trip. Statement one alone is sufficient to answer the question. We can eliminate answer choices B, C, and E.
Statement Two Alone:
y = x + 10
While statement two gives us the relationship between the two variables, it does not allow us to determine a numerical value for either of them. Thus, we cannot determine the average speed for the entire trip.