princejmy
A person traveled 100mi. What is the average rate during the entire trip?
1) The average rate during the first 60 mi was 50 mph.
2) The average rate during the last 60 mi as 50 mph.
Hi. This is my first post. This question is directly from a GMAT that I just took on Tuesday. I know in general, you take the total distance and divide it by the added up times in each section, but I've never seen a rate question where the information overlapped. Thanks. Alternatively, what would be the answer if the second piece of information said 40 mph instead of 50.
Dear
princejmyI'm happy to respond.
As always, this is an interesting problem: the problems on the real GMAT are fantastic!
Let's consider the two statements combined.
Scenario #1 is one in which the person traveled at a constant velocity of 50 mph for the entire trip. Thus, we know the average rate is 50 mph.
Scenario #2 is more complicated.
Divide the trip into PQ = the first 40 miles, QR = the middle 20 miles, and RS = the last 40 miles.
Average speed in the first 60 miles, PQ + QR, is 50 mph, so the time of this interval is 1.2 hr
Average speed in the last 60 miles, QR + RS, is 50 mph, so the time of this interval is also 1.2 hr
Suppose the person went 100 mph on QR, so the time is simply 0.2 hrs on that interval. Then suppose the person went 40 mph on PQ and RS, so each of these take 1 hr. Thus, it would be the case that the first 60 mi and the last 60 mi each would take 1.2 hrs, and thus have a rate of 50 mph.
The total trip would be covered in 2.2 hrs, and (100 mi)/(2.2 hr) equals something other than 50 mph.
Two scenarios, consistent with both statements, produces two different numerical answers to the prompt question, so the answer is (E).
Changing 50 mph to 40 mph in one of the statements would keep the answer at (E).
Does all this make sense?
Mike