4 mph
Step-by-step explanation
Step 1
let x represents the speed when she bicycle
let y represents the speed when she walks
so,
A woman can bicycle 52 miles in the same time as it takes her to walk 16 miles.

and
She can ride 9 mph faster than she can walk, ( in other words you have to add 9 to the spee when she walks to obtain the speed when she runs,

Step 2
solve for y

replace the x value from equation (2) in equation (1).

so, she can walk to 4 miles per hour
I hope this helps you