charity walk where each mile waled pays more until the total is $50 for 20 miles.
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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.

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