P, Q, and R are located in 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 th 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 term of x, y, and Z?(Assume x,y, and Z are positive.)

A) sqr x^2+y^2/z
B) x+sqr x^2+y^2/z
C) y+sqr x^2+y^2/z
D) z/x+sqr x^2+y^2
E) z/y+sqr x^2+y^2





Time = Distance / Speed

Imagine a right triangle PQR where the angle Q is 90' (from the given fact that Q is due east of P and north of R).

Distance between Q and R is y as given in the question and speed is Z, also given in the question. Therefore time from Q to R is y/Z.

Distance between R and P can be derived from Pythagorean Theorem because the angle Q = 90'.
By using the Theorem, distance between R and P is sqrt(x^2 + y^2). Speed from R to P is Z which is given in the question.
Therefore time from R to P is (sqrt(x^2 + y^2))/Z.

By simply adding the two, y/Z + (sqrt(x^2 + y^2))/Z = (y + sqrt(x^2 + y^2))/Z.

Ans C