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P, Q and R are located in a flat region of a certain state.
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Updated on: 21 Jun 2014, 10:34
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P, Q and R are located in a flat region of a certain state. Q is x miles due east of P and y miles due north of R. Each pair of points is connected by a straight road. What is the number of hours needed to drive from Q to R and then from R to P at a constant rate of z miles per hour, in terms of x, y and z? (Assume x, y, and z are positive) A. \(\frac{\sqrt{x^2+y^2}}{z}\) B. \(\frac{x+\sqrt{x^2+y^2}}{z}\) C. \(\frac{y+ \sqrt{x^2+y^2}}{z}\) D. \(\frac{z}{x+\sqrt{x^2+y^2}}\) E. \(\frac{z}{y+\sqrt{x^2+y^2}}\)
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Originally posted by Poots on 18 Oct 2008, 20:04.
Last edited by Bunuel on 21 Jun 2014, 10:34, edited 1 time in total.
Renamed the topic, edited the question and added the OA.




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Re: P, Q and R are located in a flat region of a certain state.
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21 Jun 2014, 10:35
MensaNumber wrote: are the answer choices correctly written here? My answer would be (x^2+y^2)^1/2 + y / z Edited the answer choices. P, Q and R are located in a flat region of a certain state. Q is x miles due east of P and y miles due north of R. Each pair of points is connected by a straight road. What is the number of hours needed to drive from Q to R and then from R to P at a constant rate of z miles per hour, in terms of x, y and z? (Assume x, y, and z are positive)A. \(\frac{\sqrt{x^2+y^2}}{z}\) B. \(\frac{x+\sqrt{x^2+y^2}}{z}\) C. \(\frac{y+ \sqrt{x^2+y^2}}{z}\) D. \(\frac{z}{x+\sqrt{x^2+y^2}}\) E. \(\frac{z}{y+\sqrt{x^2+y^2}}\) Points are located as shown below: PQ   R So we have the right triangle: \(PQ=x\) and \(QR=y\). \(PR=hypotenuse=\sqrt{x^2+y^2}\). Total distance to cover: \(y+\sqrt{x^2+y^2}\) > \(time=\frac{distance}{rate}=\frac{y+\sqrt{x^2+y^2}}{z}\). Answer: C.
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Re: P, Q and R are located in a flat region of a certain state.
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18 Oct 2008, 21:39
Poots wrote: P, Q and R are located in a flat region of a certain state. Q is x miles due east of P and y miles due north of R. Each pair of points is connected by a straight road. What is the number of hours needed to drive from Q to R and then from R to P at a constant rate of z miles per hour, in terms of x, y and z? (Assume x, y, and z are positive)
a. √x² + y² / z b. x + √ x² + y² / z c. y + √x² + y² / z d. z / x + √x² + y² e. z / y + √x² + y² RP= (x^2+y^2)^1/2 QR=y speed =z total time =total dist /speed = (x^2+y^2)^1/2 + y / z IMO C
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Re: P, Q and R are located in a flat region of a certain state.
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22 Oct 2008, 16:26
Thanks spriya.
Does anyone have another explanation for this?
Thanks!



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Re: P, Q and R are located in a flat region of a certain state.
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22 Oct 2008, 16:45
Thanks LS, I guess the more detailed follow up question would be: How do you get this for RP? spriya wrote: RP= (x^2+y^2)^1/2



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Re: P, Q and R are located in a flat region of a certain state.
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22 Oct 2008, 16:52
Oh ok,
If you draw the points, you will get PQR as a right angled traingle with sides as x, y, sqrt(x^2 + y^2)
And we need to the find the time required to travel the distances y and sqrt(x^2+y^2)



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Re: P, Q and R are located in a flat region of a certain state.
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22 Oct 2008, 17:03
Epiphany! Thanks LS.



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Re: P, Q and R are located in a flat region of a certain state.
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21 Jun 2014, 07:56
are the answer choices correctly written here? My answer would be (x^2+y^2)^1/2 + y / z
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Re: P, Q and R are located in a flat region of a certain state.
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10 Sep 2017, 23:24
It forms a right angle triangle Base (x) (PQ) and Height (y)(QR)
Hypotenus(PR) sqrt (x^2+y^2)
So total distance: y+ sqrt (x^2+y^2)/z



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Re: P, Q and R are located in a flat region of a certain state.
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11 Sep 2017, 15:00
Poots wrote: P, Q and R are located in a flat region of a certain state. Q is x miles due east of P and y miles due north of R. Each pair of points is connected by a straight road. What is the number of hours needed to drive from Q to R and then from R to P at a constant rate of z miles per hour, in terms of x, y and z? (Assume x, y, and z are positive)
A. \(\frac{\sqrt{x^2+y^2}}{z}\)
B. \(\frac{x+\sqrt{x^2+y^2}}{z}\)
C. \(\frac{y+ \sqrt{x^2+y^2}}{z}\)
D. \(\frac{z}{x+\sqrt{x^2+y^2}}\)
E. \(\frac{z}{y+\sqrt{x^2+y^2}}\) We see that P, Q, and R form the vertices of a right triangle, with Q as the vertex of the right angle. Furthermore, PQ = x and QR = y are the legs of the right triangle, and RP is the hypotenuse of the right triangle. Thus, if we let RP = n, then by the Pythagorean theorem we have: n^2 = x^2 + y^2 n = √( x^2 + y^2) Since time = distance/rate, it takes y/z hours to drive from Q to R and √( x^2 + y^2)/z hours to drive from R to P. So, the total driving time is [y + √( x^2 + y^2)]/z. Answer: C
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Re: P, Q and R are located in a flat region of a certain state.
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01 Apr 2018, 06:22
Bunuel Please provide a detailed pictorial explanation. Hard to understand how there is a right triangle. Thanks.



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Re: P, Q and R are located in a flat region of a certain state.
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01 Apr 2018, 06:51
sadikabid27 wrote: Bunuel Please provide a detailed pictorial explanation. Hard to understand how there is a right triangle. Thanks. Hi sadikabid27Since the point Q is 1. y miles due north of R 2. x miles due east of P and are connected via straight roads, the points PQR form a rightangled triangle Please find the pictorial representation Attachment:
Diagram.png [ 3.17 KiB  Viewed 1582 times ]
Hope this helps you!
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P, Q and R are located in a flat region of a certain state.
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03 Jul 2018, 04:11
Bunuel wrote: MensaNumber wrote: are the answer choices correctly written here? My answer would be (x^2+y^2)^1/2 + y / z Edited the answer choices. P, Q and R are located in a flat region of a certain state. Q is x miles due east of P and y miles due north of R. Each pair of points is connected by a straight road. What is the number of hours needed to drive from Q to R and then from R to P at a constant rate of z miles per hour, in terms of x, y and z? (Assume x, y, and z are positive)A. \(\frac{\sqrt{x^2+y^2}}{z}\) B. \(\frac{x+\sqrt{x^2+y^2}}{z}\) C. \(\frac{y+ \sqrt{x^2+y^2}}{z}\) D. \(\frac{z}{x+\sqrt{x^2+y^2}}\) E. \(\frac{z}{y+\sqrt{x^2+y^2}}\) Points are located as shown below: PQ   R So we have the right triangle: \(PQ=x\) and \(QR=y\). \(PR=hypotenuse=\sqrt{x^2+y^2}\). Total distance to cover: \(y+\sqrt{x^2+y^2}\) > \(time=\frac{distance}{rate}=\frac{y+\sqrt{x^2+y^2}}{z}\). Answer: C. Bunuel we are asked to find Q to R and R to P , in other words TWO LINES , why do you use \(PQ=x\) and where from do you get Y which is not under radical sign ? \(y+\sqrt{x^2+y^2}\) thank you



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Re: P, Q and R are located in a flat region of a certain state.
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03 Jul 2018, 07:34
dave13 wrote: Bunuel wrote: MensaNumber wrote: are the answer choices correctly written here? My answer would be (x^2+y^2)^1/2 + y / z Edited the answer choices. P, Q and R are located in a flat region of a certain state. Q is x miles due east of P and y miles due north of R. Each pair of points is connected by a straight road. What is the number of hours needed to drive from Q to R and then from R to P at a constant rate of z miles per hour, in terms of x, y and z? (Assume x, y, and z are positive)A. \(\frac{\sqrt{x^2+y^2}}{z}\) B. \(\frac{x+\sqrt{x^2+y^2}}{z}\) C. \(\frac{y+ \sqrt{x^2+y^2}}{z}\) D. \(\frac{z}{x+\sqrt{x^2+y^2}}\) E. \(\frac{z}{y+\sqrt{x^2+y^2}}\) Points are located as shown below: PQ   R So we have the right triangle: \(PQ=x\) and \(QR=y\). \(PR=hypotenuse=\sqrt{x^2+y^2}\). Total distance to cover: \(y+\sqrt{x^2+y^2}\) > \(time=\frac{distance}{rate}=\frac{y+\sqrt{x^2+y^2}}{z}\). Answer: C. Bunuel we are asked to find Q to R and R to P , in other words TWO LINES , why do you use \(PQ=x\) and where from do you get Y which is not under radical sign ? \(y+\sqrt{x^2+y^2}\) thank you You don't read questions carefully enough. The question asks to find the number of hours need to drive from Q to R and then from R to P at a constant rate of z miles per hour, NOT the distance. Total distance to cover (in blue): \(y+\sqrt{x^2+y^2}\) > \(time=\frac{distance}{rate}=\frac{y+\sqrt{x^2+y^2}}{z}\). Attachment:
Untitled.png [ 4.79 KiB  Viewed 1010 times ]
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