James and Henry are at the northwest corner of their...

[BTGmoderatorLU]

James and Henry are at the northwest corner of their business school's football field, which is a rectangle 300 ft long and 160 ft wide. James walks in a straight line directly to the southeast corner of the field. If Henry walks 180 ft down the west side of the field and then walks in a straight line directly to the southeast corner of the field, how many feet farther, to the neareast 10 ft, will Henry walk than James?

A. 20
B. 40
C. 80
D. 120
E. 140

The OA is B.

I know that I can determine the distance covered by James using the dimensions of the field and the Pythagoras's theorem, then

$$\sqrt{\left(300\right)^2+\left(160\right)^2}$$

But, I don't understand how can I determine the distance covered by Henry.

Experts, can you help assist me with this PS question, please? Thanks!

[EconomistGMATTutor]

Hello LUANDATO.

What you said is correct. James walked $$\sqrt{\left(300\right)^2+\left(160\right)^2}=340\ ft.$$ Henry walked 180 ft down and then walked in a straight line directly to the southeast corner. We have a right triangle with cathetus a=300-180=120 and b=160. So, the length of the hypotenuse is $$\sqrt{\left(120\right)^2+\left(160\right)^2}=200\ ft.$$ This implies that Henry walked 200+180=380 ft. That is to say, Henry walked 40 ft more than James. This is why the correct answer is B.

I hope this may help you.

I'm available if you'd like a follow-up.

Regards.