see the attached figure to better understand the problem
Let
z---------> distance from the library to the park in miles
x-------> distance from the park to the to the football field in miles
y-------> distance from the park to Kathy's home in miles
we know that
In the right triangle ABC
Applying the Pythagorean Theorem
-----> equation
In the right triangle ABD
Applying the Pythagorean Theorem
-----> equation
In the right triangle BCD
Applying the Pythagorean Theorem
-----> equation
Add equation
and equation


-----> equation 
Substitute equation
in equation 

Find the value of x

therefore
the answer is
Part a) The distance from the library to the park is equal to 
Part b) The distance from the park to the to the football field is equal to 