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Truck A is on a straight highway heading due south at the same time T

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Truck A is on a straight highway heading due south at the same time T  [#permalink]

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New post 13 Jan 2015, 16:44
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Truck A is on a straight highway heading due south at the same time Truck B is on a different straight highway heading due east. At 1:00 PM, Truck A is exactly 14 miles north of Truck B. If both trucks are traveling at a constant speed of 30 miles per hour, at which of the following times will they be exactly 10 miles apart?

A. 1:10 PM
B. 1:12 PM
C. 1:14 PM
D. 1:15 PM
E. 1:20 PM
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Truck A is on a straight highway heading due south at the same time T  [#permalink]

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New post 13 Jan 2015, 23:40
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viktorija wrote:
Truck A is on a straight highway heading due south at the same time Truck B is on a different straight highway heading due east. At 1:00 PM, Truck A is exactly 14 miles north of Truck B. If both trucks are traveling at a constant speed of 30 miles per hour, at which of the following times will they be exactly 10 miles apart?

A. 1:10 PM
B. 1:12 PM
C. 1:14 PM
D. 1:15 PM
E. 1:20 PM


Quickly draw to understand what the question is telling you. The first diagram shown you the situation at 1:00 pm. The second diagram shows the pic of some time later:
Attachment:
Ques3.jpg
Ques3.jpg [ 9.52 KiB | Viewed 2187 times ]


The hypotenuse of 10 should remind you of the 3-4-5 pythagorean triplet. Here we might have its multiple 6-8-10.
So we are looking at the vertical distance of 8 (which means truck A has traveled a distance of 6 miles from the 14 miles) and horizontal distance of 6 traveled by truck B - both trucks traveled 6 miles in this case which is expected since their speed is the same.
They travel 30 miles in one hour (60 mins) so they will travel 6 miles in 60*6/30 = 12 mins.

Answer (B)
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Re: Truck A is on a straight highway heading due south at the same time T  [#permalink]

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New post 13 Jan 2015, 17:41
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viktorija wrote:
Truck A is on a straight highway heading due south at the same time Truck B is on a different straight highway heading due east. At 1:00 PM, Truck A is exactly 14 miles north of Truck B. If both trucks are traveling at a constant speed of 30 miles per hour, at which of the following times will they be exactly 10 miles apart?

A. 1:10 PM
B. 1:12 PM
C. 1:14 PM
D. 1:15 PM
E. 1:20 PM


I went down the answer choices.

B. at 1:12pm 12 minutes went by, or 1/5th of an hour.

30mph = distance / (1/5)
distance = 6 miles

Truck A's coordinates: (0, 14-6) = (0, 8)
Truck B's coordinates: (6, 0)

\sqrt{(8-0)^2 + (0-6)^2}
\sqrt{64+36}
\sqrt{100}
\sqrt{10}

The answer is 12 minutes passed for the trucks to be 10 miles apart.
B.
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Re: Truck A is on a straight highway heading due south at the same time T  [#permalink]

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New post 13 Jan 2015, 21:50
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Hi viktorija,

BassanioGratiano has shown how TESTing THE ANSWERS can be used to solve this problem. Here's another pattern-based approach.

This prompt describes the paths traveled by 2 trucks - if you were to draw a series of pictures that were based on the distances and speeds described over time (from 1pm onward), you would end up with a series of RIGHT TRIANGLES.

The GMAT commonly tests a set of established right triangles - 30/60/90, 45/45/90, 3/4/5 and 5/12/13. Here, we're asked for the time at which the trucks are 10 miles apart. Since the question doesn't describe angles of any kind, and 10 is a multiple of 5, we're almost certainly looking for a 3/4/5 triangle that's been doubled (into a 6/8/10 triangle).

At 1:00pm, Truck A is 14 miles NORTH of Truck B. Truck A is traveling SOUTH, Truck B is traveling East - they're both traveling 30miles/hour. This means that every 2 minutes = 1 mile traveled.

We can now make a quick table comparing the "sides of the triangle" that would be created by the two trucks:
A|B
13|1 Not a 6/8/10
12|2 Not a 6/8/10
11|3 Not a 6/8/10
10|4 Not a 6/8/10
9|5 Not a 6/8/10
8|6 !!!!!This IS a 6/8/10!!!!!!

Since each Truck traveled 6 miles, and 1 mile = 2 minutes, we know that the trucks traveled 6(2) = 12 minutes. At 1:12pm, the trucks are exactly 10 miles apart.

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Re: Truck A is on a straight highway heading due south at the same time T  [#permalink]

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New post 13 Jan 2015, 23:25
that was pretty good explanation EMPOWERgmatRichC
Kudos to you
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Re: Truck A is on a straight highway heading due south at the same time T  [#permalink]

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New post 24 Dec 2015, 11:00
let each truck travel m miles, creating a right triangle with sides of 14-m, m, and a hypotenuse of 10
(14-m)^2+m^2=10^2
(m-8)(m-6)=0
m=8 and 6 miles
8/30=4/15 hour=1:16
6/30=1/5 hour=1:12, answer B
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Re: Truck A is on a straight highway heading due south at the same time T  [#permalink]

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