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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. \(\frac{z}{y+\sqrt{x^2+y^2}}\)
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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21 Jun 2014, 11:35
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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. \(\frac{z}{y+\sqrt{x^2+y^2}}\)
Points are located as shown below:
P----Q
------
------
-----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.
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:
P----Q
------
------
-----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.
General Discussion
11 Sep 2017, 16:00
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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
