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

S= z (y-x)/(x+y)

Explanation:

Lets the speed of high speed train = u

Lets the regular speed train = v

We know that

Distance = Speed x time

For high speed train

z = u .x

u= z/x ----------1

For regular speed train

z = v .y

v = z/y -------------2

Both are traveling in opposite direction so relative speed

Vr = z / x+ z /y

Lets in time t they will meet

z = (z / x+ z /y) t

t= xy/ (x+y)

Lets take distance cover by high speed train is m when it moves A to B and speed cover by regular train is n when it is moving B to A.They meet at time t.

m = u .t

m = z / x .xy/ (x+y)

m = zy/ (x+y) -----------3

n = v .t

n = z / y .xy/ (x+y)

n = zx/ (x+y) -----------4

From equation 3 and 4

So

m - n= zy/ (x+y) - zx/ (x+y)

S= z (y-x)/(x+y)

Option a is correct.