let

s = the length of the side of the softball field (the distance between the bases) assuming it is a square

b = the length of the side of the baseball field ( he distance between the bases) assuming it is a square

the perimeter of a softball field is 2/3 of the perimeter of a baseball diamond means

4s = (2/3)(4b) divide both sides by 4

s = (2/3)b

Together, the two perimeters measures 200 yds:

4s + 4b = 200 divide both sides by 4

s + b = 50

by solving the system of equations:

s = (2/3)b

s + b = 50

we find:

s = 20 yd

b = 30 yd

click here to see the step by step solution of the system of equations:

the distance between the bases of the softball field is 20 yd.

the distance between the bases of the baseball field is 30 yd.