Since the bicyclist, travels 8 miles due west and then moves towards a point northwards of the point from which he started.
He has given the distance traveled in order to reach the point north as x(which is y miles from original location)
So, it basically forms a right angled triangle with a hypotenuse x, sides y, and 8
Applying Pythagoras theorem, \(x^2 = y^2 + 8^2 => x^2 - y^2 = 64\)
which is possible in 2 cases {(x=10,y=6) or (x=17,y=15)} as \((x-y)(x+y) = 64\)
Case 1: The other sides are x=10 and y=6 because 16*4 = 64.
The sum of the distance walked is \(8+x+\frac{x}{2} = 8+6+2 = 16\), which is not available in the answer options.
Case 2: The only other possibility is 17 and 15, where x=17 and y=15.
So, total distance traveled will be \(8+x+\frac{x}{2} = 8+17+\frac{17}{2} = 25+8.5 = 33.5\)
(Option D)
_________________
You've got what it takes, but it will take everything you've got