A: There are 9 Unique Solutions
1:   3 / 15 = 0.2
2:   6 / 12 = 0.5
3:   6 / 15 = 0.4
4:   7 / 14 = 0.5
5:   7 / 35 = 0.2
6:   8 / 16 = 0.5
7:   9 / 15 = 0.6
8:   9 / 18 = 0.5
9:   9 / 45 = 0.2

Q: Mr. Cawley biked 10 miles in half an hour with the wind at his back. Returning against the wind, the trip was 40 minutes.
On a windless day, how long would it take him to bike the 10 miles?

A: The two equations are both based on d = rt
(although below they are written as t multiplied by the rate).

r = the rate without the wind in mph
w = rate of the wind in mph

First we have to find the r without the wind.
1/2 (r + w) = 10 multiply by 2 r + w = 20
2/3 (r – w) = 10 multiply by 3/2 r – w = 15

2r = 35
r = 17.5
w = 2.5

To find the rate at which he biked the 10 miles, we use d = rt again
10 = 17.5 t
so time = 10/17.5 hours which when we mulitply by 60 to get minutes, our answer is 34 2/7 minutes.

The first three lines all have a common sum. When applying this common sum to 5*5 it equals 2.