the speed of train A is 14 mph slower than train B. Train A travels 190 miles in the same time it takes train B to travel 260 miles. What is the speed of each train?

V mi/h = Speed of B.

(V-14) = Speed of A.

Eq1: V*T = 260 = Dist. of B.
T = 260/V.

Eq2: (V-14)T = 190 = Dist. of A.
In Eq2, replace T with 260/V:
(V-14)260/V = 190.
Multiply both sides by V:
(V-14)260 = 190V
260V - 3640 = 190V
260V-190V = 3640
70V = 3640
V = 52 mi/h
(V-14) = 38 mi/h.

To find the speed of each train, let's assign variables. Let the speed of train A be represented by "x" mph and the speed of train B be represented by "y" mph.

The problem states that train A is 14 mph slower than train B. Hence, we can set up the equation:

x = y - 14 (Equation 1)

The problem also mentions that train A travels 190 miles in the same time it takes train B to travel 260 miles. This implies that the time taken by both trains is the same.

We can use the formula: Time = Distance / Speed to set up another equation:

190 / x = 260 / y (Equation 2)

Now, we have a system of two equations (Equation 1 and Equation 2) that we can solve simultaneously to find the values of x and y.

To solve the system of equations, we can use the substitution method. Rearrange Equation 1 to express y in terms of x:

y = x + 14 (Equation 3)

Now substitute Equation 3 into Equation 2:

190 / x = 260 / (x + 14)

To simplify, cross-multiply:

190 * (x + 14) = 260 * x

Expand and simplify further:

190x + 2660 = 260x

Subtract 190x from both sides:

2660 = 70x

Divide both sides by 70:

x = 38

Now substitute the value of x back into Equation 3 to find y:

y = 38 + 14

y = 52

Therefore, the speed of train A is 38 mph, and the speed of train B is 52 mph.