Question

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) z(y – x)/x + y
(B) z(x – y)/x + y
(C) z(x + y)/y – x
(D) xy(x – y)/x + y
(E) xy(y – x)/x + y

Answer 1

B

Explanation:

To solve this, we use ratio.

Firstly, we need to know the number of hours traveled. The total number of hours traveled = x+y

Ratio of this used by high speed train = x/(x +y).

Total distance traveled before they meet = [x/(x + y)] × z

For low speed train = [y/(x + y)] × z.

The difference would be distance by high speed train - distance by low speed train.

= z [ (x - y)/x + y)]