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# Peter and Jacob are at the northwest corner of a field, which is a rec

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Math Expert
Joined: 02 Sep 2009
Posts: 52108
Peter and Jacob are at the northwest corner of a field, which is a rec  [#permalink]

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15 Apr 2015, 03:49
00:00

Difficulty:

95% (hard)

Question Stats:

34% (03:08) correct 66% (03:27) wrong based on 86 sessions

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Peter and Jacob are at the northwest corner of a field, which is a rectangle 300 ft long and 160 ft wide. Peter walks in a straight line directly to the southeast corner of the field. If Jacob 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, what is the difference in the distance traveled by the two?

(A) 20
(B) 40
(C) 80
(D) 120
(E) 140

Kudos for a correct solution.

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Re: Peter and Jacob are at the northwest corner of a field, which is a rec  [#permalink]

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15 Apr 2015, 07:51
Bunuel wrote:
Peter and Jacob are at the northwest corner of a field, which is a rectangle 300 ft long and 160 ft wide. Peter walks in a straight line directly to the southeast corner of the field. If Jacob 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, what is the difference in the distance traveled by the two?

(A) 20
(B) 40
(C) 80
(D) 120
(E) 140

Kudos for a correct solution.

Distance by Peter=Diagonal of the rectangle of 300*160 ft
$$\sqrt{90000+25600}$$
$$\sqrt{115600}$$
=340

Distance by Jacob = 180 + Diagonal of rectangle of 300*20 ft
=180 + $$\sqrt{90000+400}$$
=180+approx 300
=480 approx

Difference between the distance of Peter and Jacob = 480-340
=140

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Joined: 01 Jan 2015
Posts: 56
Re: Peter and Jacob are at the northwest corner of a field, which is a rec  [#permalink]

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15 Apr 2015, 13:37
1
So Peter's distance = diagonal of the rectangle = sq root(300x300 + 160x160) = 340
Jacob's distance = 180+ sq root(120x120 + 160x160) = 180+200 = 380
Difference = 380-340 = 40
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Joined: 18 Dec 2014
Posts: 99
Re: Peter and Jacob are at the northwest corner of a field, which is a rec  [#permalink]

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17 Apr 2015, 02:03
1
Peter and Jacob are at the northwest corner of a field, which is a rectangle 300 ft long and 160 ft wide. Peter walks in a straight line directly to the southeast corner of the field. If Jacob 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, what is the difference in the distance traveled by the two?

(A) 20
(B) 40
(C) 80
(D) 120
(E) 140

Distance Peter:
300^2 + 160^2 = \sqrt{115600} -> 340

Distance Jacob:
120^2 + 160^2 = \sqrt{40000} -> 200
200 + 180 = 380

380 - 340 = 40. B.
Math Expert
Joined: 02 Sep 2009
Posts: 52108
Re: Peter and Jacob are at the northwest corner of a field, which is a rec  [#permalink]

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20 Apr 2015, 05:06
1
1
Bunuel wrote:
Peter and Jacob are at the northwest corner of a field, which is a rectangle 300 ft long and 160 ft wide. Peter walks in a straight line directly to the southeast corner of the field. If Jacob 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, what is the difference in the distance traveled by the two?

(A) 20
(B) 40
(C) 80
(D) 120
(E) 140

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION

The first thing we do in these “direction” questions is draw the diagram. But there is a problem here: how do we decide the orientation of the rectangle? It could be either of these two.
Attachment:

Ques5.jpg [ 9.54 KiB | Viewed 1138 times ]

A few things help us decide this. 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 width isn’t (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, one could make the rectangle on the left and there will be no conflict. But the question maker may not want to take for granted that you know this.

So he/she leaves a clue – the question mentions that ‘Jacob walks 180 ft down the west side of the field’. There needs to be at least 180 ft on the west side of the field for him to travel that much. So the orientation on the left makes sense. This is something the question maker would have put to try to give you a hint of the orientation. Now that we know what our diagram should look like, we can proceed to solve this question.
Attachment:

Ques4.jpg [ 10.63 KiB | Viewed 1139 times ]

If you just remember some of your pythagorean triplets, this question can be solved in moments (and that’s why we suggest you to remember them!) If not, it would involve some calculations.

QR = 160, RS = 300

So QR:RS = 8:15

Remember 8-15-17 pythagorean triplet? (the third triplet after 3-4-5 and 5-12-13)

Since the two sides are in the ratio 8:15, the hypotenuse must be 17. The common multiplier is 20 so QS should be 17*20 = 340

Therefore, Peter traveled 340 feet.

TP = 120, PS = 160

TP:PS = 3:4

Does it remind you of 3-4-5 triplet?

120 is 3*40 and 160 is 4*40 so TS will be 5*40 = 200

So Jacob traveled a total distance of 180 + 200 = 380 feet.

Difference between the distance traveled = 380 – 340 = 40 feet

Note: The following triplets come in handy: (3, 4, 5) (5, 12, 13) (8, 15, 17) (7, 24, 25) (20, 21, 29) and (9, 40, 41)
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Re: Peter and Jacob are at the northwest corner of a field, which is a rec  [#permalink]

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17 Feb 2017, 21:37
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Re: Peter and Jacob are at the northwest corner of a field, which is a rec &nbs [#permalink] 17 Feb 2017, 21:37
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