math help please! only 1 question?

Question

A rectangular garden 30 m by 40 m has two paths of equal width crossing through. Which of the following widths must each path measure if the total area covered by the paths is 325 m2?


A.
The width of each path is 8 m.

B.
The width of each path is 15 m.

C.
The width of each path is 5 m.

D.
The width of each path is 10 m.

Answer 1

area of the path=(30+40)w-w^2
-w^2+70w=325
w^2-70w+325=0
(w-5)(w-65)=0
w=5 or 65
rejecting 65
w=5 m

Answer 2

325m^2-2 paths/30 meters each=325/60=5.41m if the paths cross the widths
if the cross the length 325/2/40=4.0625m since 4 isn't a choice, I assume the paths cross the width & are 5m wide
answer C

Answer 3

Crossing which way? Parallel to each of the sides? If we assume that, then you have one path that has an area of 30n and another with an area of 40n, except they cross at an area of n², where n is the width of each of the paths (in meters). So that you don't double count the area where they cross, you have to subtract n².

Writing it as an equation you would have:

30n + 40n - n² = 325

Putting everything on one side you have:
70n - n² = 325
70n = n² + 325
0 = n² - 70n + 325
n² - 70n + 325 = 0

Factoring:
(n - 65)(n - 5) = 0

So either the path is 65 meters or 5 meters wide. One is unreasonable given that the garden is only 30m x 40m, so the correct answer is:

c. The width of each path is 5m.