Problem Solving

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

OA after some discussions.
can anyone tell me what does this line mean? to the nearest 10 ft

Resp007 wrote: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

James = PINK line:
James walks from B to D.
∆ABD is a multiple of an 8:15:17 triangle:
20 * (8:15:17) = 160:300:340.
Since BD=340, the distance traveled by James = 340 feet.

Henry = BLUE lines:
Henry walks south 180 feet from B to E.
Since AB=300, BE=180 and AE=120.
After he arrives at E, Henry walks from E to D.
∆AED is a multiple of a 3:4:5 triangle:
40 * (3:4:5) = 120:160:200.
Since DE=200, the total distance walked by Henry = 180+200 = 380 feet.

Henry's distance - James's distance = 380-340 = 40.

The correct answer is B.

HI Mitch,

The question never asked when they meet. It says when they are to the nearest 10 feet.
Or
If you can please tell me what does the following line mean?
how many feet farther, to the nearest 10 ft, will Henry walk than James?

Thanks
Resp007

Answer [spoiler]{B}[/spoiler]

Resp007 wrote:HI Mitch,

The question never asked when they meet. It says when they are to the nearest 10 feet.
Or
If you can please tell me what does the following line mean?
how many feet farther, to the nearest 10 ft, will Henry walk than James?

Thanks
Resp007

From the question prompt:
James and Henry are at the northwest corner (point B).
James walks in a straight line directly to the southeast corner (point D).
Henry walks...to the southeast corner (point D).
Since James and Henry both walk to the southeast corner, they meet at point D.

How many feet farther...will Henry walk than James?
To walk FARTHER is to walk a GREATER DISTANCE.
Since James walks in a straight line and Henry takes a less direct route, Henry walks farther than James.
The question stem asks for the DIFFERENCE between the distance traveled by Henry and that traveled by James.

To the nearest 10 feet implies that the difference between the two distances can be approximated.
I suspect that this phrase is included because the dimensions of the field (300 feet and 160 feet) can lead to some messy arithmetic.
But approximation is not necessary here.
As shown in my solution above, the exact difference between Henry's distance and James's distance can be calculated quickly if we recognize that ∆ABD is a multiple of an 8-15-17 triangle and that ∆ADE is a multiple of a 3-4-5 triangle.

Resp007 wrote:HI Mitch,

The question never asked when they meet. It says when they are to the nearest 10 feet.
Or
If you can please tell me what does the following line mean?
how many feet farther, to the nearest 10 ft, will Henry walk than James?

Thanks
Resp007

Hi Resp007,
to the nearest 10 ft mean,

if we got answer as 12 then nearest 10 mean answer is 10
if we got answer as 17 then nearest 10 mean answer is 20

In-other words, Approximate to nearest 10's

Regards,
Uva.

Oh dude... :/

Thanks Mitch and Uva. These kind of wordings in the question stem they just throw me off track.
I drew the diagram somewhat like this and you can imagine the fuss.
Stupid me.

A = NW corner
B = Henry's turning point
C = SW corner
D = SE corner

Using Pythagoras' theorem:

AD^2 = AC^2 + CD^2
AD^2 = 160^2 + 300^2
So right angle triangle ACB has hypotenuse AD = 340

Also
BD^2 = BC^2 + CD^2
BD^2 = 120^2 + 160^2
So right angle triangle BCD has hypotenuse AD = 200

Harry travels distance AB + BD = 180 + 200 = 380
James travels distance AD = 340
Difference = 380 - 340 = 40

Answer B

Resp007 wrote:Oh dude... :/

Thanks Mitch and Uva. These kind of wordings in the question stem they just throw me off track.
I drew the diagram somewhat like this and you can imagine the fuss.
Stupid me.

Ha ha:) It happens at the initial stage.

Regards,
Uva.

This was was easy to solve but how do we get this one in 2 minutes .I took me a 1.5 minutes just to understand what the problem was asking