If the first mile pays $a, then the second and subsequent miles pay $b more than the one before, and we have a+a+b+a+2b+a+3b+...until the amount reaches $50. Since 20 miles are walked the last mile earns a+19b. We take the amount earned in pairs: (a+a+19b)+(a+b+a+18b)+(a+2b+a+17b)+... Each pair adds up to 2a+19b, and there are 10 pairs, so the total is 20a+190b=50. Therefore 2a+19b=5. We can write b=(5-2a)/19. Since b must be positive 2a<5, a<$2.50, that is, payment for the first mile is less than $2.50. If a=$0.22, then b=$0.24. So the payment builds up: 22c for the first mile, 46c for the second mile, 70c for the third mile, 94c for the fourth mile, and so on.
There are many possible answers. a=$0.41, b=$0.22; a=$0.60, b=$0.20, etc., all controlled by the equation 2a+19b=5.
a($) |
b(c) |
0.22 |
24 |
0.41 |
22 |
0.60 |
20 |
0.79 |
18 |
0.98 |
16 |
1.17 |
14 |
1.36 |
12 |
1.55 |
10 |
1.74 |
8 |
1.93 |
6 |
2.12 |
4 |
2.31 |
2 |
For example, if the first mile pays $0.60, the next mile pays $0.80, then $1, $1.20, until after 20 miles the total comes to $50.