James and Henry are at the northwest corner of their busines

Question

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 nearest 10 ft, will Henry walk than James?

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

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

Bunuel · Answer

Look at the diagram below: Football field.png The distance covered by James (AD) is shown in blue and it equals to \sqrt{300^2+160^2}=\sqrt{10^2(30^2+16^2)}=10*\sqrt{1156}=340 ; The distance covered by Henry (AB+BD) is shown in red and it equals to 180+\sqrt{120^2+160^2}=180+\sqrt{10^2(12^2+16)^2}=180+10\sqrt{400}=380 ; The difference is 380-340=40. Answer: B.

gmatbull · Answer

Thanks Bunuel for your lucid explanations as usual.
I misinterpreted the text below:
"If Henry walks 180 ft down the west side of the field " to mean
"Henry walks 180 ft westwards"; Sure, that was a misleading interpretation.

Actually, Henry walked DOWNWARD, but on the western wing of the field.

rashmilagisetty · Answer

How do we decide the rectangle layout to be? I took 300 to be the length from northeast to east whereas in the explanation it takes 160 for the same length.

gmatbull · Answer

Which ever orientation u prefer doesn't change the fact that it remains a rectangle as shown in the attached.
However, note that If Henry walks  180 ft down the west side of the field , the 
vertical side must be the side with 300 ft.

Bunuel · Answer

Bumping for review and further discussion.

Infinitive · Answer

So what does this sentence mean please?

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 nearest 10 ft, will Henry walk than James?

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

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

This is the only sentence that put me off that I didnt understand.

Bunuel · Answer

I guess the question intends us to do some approximations to get the correct answer but as you can see we can get the exact answer quite easily, thus approximation is not necessary.

np1986 · Answer

Is there an alternative (and quicker) way to get the solution without doing the calculations, e.g. through ballparking and eliminating answer options?

KarishmaB · Answer

Actually, the method shown by Bunuel is quite straight forward and you don't need to do any calculations if you just remember some of your pythagorean triplets (and that's why we suggest you to remember them!)

BC = 120, CD = 160
BC:CD = 3:4 
Does it remind you of 3-4-5 triplet?
120 is 3*40 and 160 is 4*40 so BD will be 5*40 = 200
So Henry traveled 180 + 200 = 380

AB = 160, BD = 300
So AB:BD = 8:15
Remember 8-15-17? (the third triplet after 3-4-5 and 5-12-13)
Hence AD should be 17*20 = 340
James traveled 340

Difference = 40

I have seen the following triplets coming in handy:
( 3, 4, 5 ) ( 5, 12, 13) ( 8, 15, 17) ( 7, 24, 25)
(20, 21, 29) and ( 9, 40, 41)

KarishmaB · Answer

That is a valid concern. Note that there are two definitions of length:
1. Length is the longest side of the rectangle. 
2. Width is from side to side and length is whatever isn't width (i.e. the side from up to down in a rectangle) (this definition is less embraced than the first one)

If the side from up to down is the longest side, then there is no conflict. 
Keeping this in mind, when drawing the figure, given that length is the longer of the two, I would make the diagram as shown by Bunuel and there will be no conflict.

np1986 · Answer

Thanks! This is quite helpful and should make the calculations much easier.

Fdambro294 · Answer

if you draw the picture correctly,

James walks the Hypotenuse of a Right Triangle with Legs of 300 and 160

Leg 1 = 8 *(20) = 160

Leg 2 = 15 * (20) = 300

This is a Pythagorean Triplet ----> 8 - 15 - 17

James will walk = 17 * (20) = 340

Henry will walk 180 vertically down.

Then he will walk the Hypotenuse of a Right Triangle with Legs of 120 and 160

This is another Pythagorean Triplet: 3 - 4 - 5

Leg 1 = 3 * (40) = 120

Leg 2 = 4 *(40) = 160

Hypotenuse = 5 * (40) = 200

Henry walks a Total of = 180 + 200 = 380

Henry walks 40 more than James -----> 380 - 340 = 40

-B-

James and Henry are at the northwest corner of their busines

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