While making a non-stop trip, a bus averaged m mph for the

[BTGmoderatorDC]

While making a non-stop trip, a bus averaged m mph for the first 5 hours and n mph, for the remaining 4 hours. What was the average speed of the bus, in mph, for the whole trip?

Stamement 1: 7.5m + 6n = 465
Statement 2: 2m + 3n = 180

OA A

Source: e-GMAT

[Ian Stewart]

The total distance traveled was 5m + 4n, and the total time was 9 hours, so the average speed we want to find is (5m + 4n)/9.

In Statement 1, if we divide by 1.5 on both sides, we get 5m + 4n = 310, so the average speed for the trip was 310/9.

From Statement 2 we can't find 5m + 4n, so we can't answer the question (and testing, say, m = 90 and n = 0, and m = 0 and n = 60, will clearly give two different answers to the question).

So the answer is A.