qr on datbootcamp: the difference between these two rate questions?

[starsbeneathme]

first question states something like:

average speed of skater down hill is 23 mph.
for the first 1/3 of the hill, average speed was 17 mph
the average speed of the second 1/3 was 15 mph.
..what was the skier's average speed for the final 1/3 of the journey?

for this question, it could be solved by doing this and solving for x.
(17 + 15 + x)/3 = 23


the next question states something like this:

a driver drives halfway to the airport, a distance of 30 miles, going 50 mph.
how fast must he go for the second 30 miles of the drive in order to meet an average speed of 60 mph?

for this one, i also tried
(50 + x)/2 = 60 .. i got 70, but the answer is 75.

To solve the second question, apparently we had to take in account of the time traveled at 50mph.


lol, my question is: what's the difference between these two problems -- why did we have to consider time in the second question, but not the first question? (i figured averaging the speeds were fine for these questions because the distances of each period in the question were the same -- aka, 1/3 distance in the first question, and 30 miles in the second question)

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[WheatLom]

The first question, the distance is the same for each speed, but we don't know how far or the time. In the second problem, we have to know how long it took for each segment, because we want to know how fast you have to go with the remaining time to average 60 miles in 1 hour. It takes longer than 30 minutes to go 30 miles at 50 mph than at 60 mph. So it would not be half and half where you divide by 2. You would have to go faster than 70 because you have to make up for the lost time.