It takes the high-speed train \(x\) hours to travel the \(z\) miles from Town \(A\) to Town \(B\) at a constant rate,

[VJesus12]

It takes the high-speed train \(x\) hours to travel the \(z\) miles from Town \(A\) to Town \(B\) at a constant rate, while it takes the regular train \(y\) hours to travel the same distance at a constant rate. If the high-speed train leaves Town \(A\) for Town \(B\) at the same time that the regular train leaves Town \(B\) for Town \(A,\) how many more miles will the high-speed train have traveled than the regular train when the two trains pass each other?

(A) \(\dfrac{z(y – x)}{x + y}\)

(B) \(\dfrac{z(x - y)}{x + y}\)

(C) \(\dfrac{z(x + y)}{y - x}\)

(D) \(\dfrac{xy(x - y}{x + y}\)

(E) \(\dfrac{xy(y - x)}{x + y}\)

Answer: A

Source: Manhattan GMAT