Q: What is the sum of the digits of the square of ?

A: 81
Using the standard multiplication algorithm, whose digit sum is 81.

Or by looking at the pattern:

 whose digit sum is 81
There is a shortcut to adding these digits
Reading from left to right, we can add the first 8 digits, 1 through 8 by making 4 pairs of 9 (1 + 8, 2 + 7, 3 + 6 and 4 + 5) making 36
Reading from right to left, we can add the last 8 digits (1- 8) the same way making 36.
Leaving the middle digit of 9.

36 + 36 + 9 = 81

Q: For the positive integers up to and including 2017, how many of those integers have at least one zero?

A:  There are  positive integers in total to consider.
No one digit numbers have a 0 (1-9).
Below is the list of the qualifying numbers:

Another solution is to exclude the numbers that do not have a zero and subtract from 2017:
9 one digit numbers
81 two digit numbers (9 x 9 : 9 choices for each digit 1-9)
729 three digit numbers (9 x 9 x 9: 9 choices for each digit 1-9)
For the numbers between 1000- 1999, there are the same amount as for the three digit numbers as they are the same numbers with a “1” in the thousands place value.
9 + 81 + 729 + 729 = 1548
2017 – 1548 = 469

Q: I drive at an average speed of 30 miles per hour to the railroad station each morning and just catch my train. On a particular morning there was a lot of traffic and at the halfway point I found I had averaged only 15 miles per hour. How fast must I drive for the rest of the way to catch my train?

A: It’s impossible. 
Let’s say that you need to go 30 miles which would take an hour.
If you were at the halfway point, 15 miles, at 15 miles per hour, you have already been traveling for an hour  to go that 15 miles — and you are only halfway there!
Sorry…you will miss your train.