Two trains, one going from Boston to New York and the other going from New York to Boston, started their trips at exactly same time. Speed of the first train was 10 miles per hour less than twice the speed of the second train. How far from Boston station have they met, if the total distance between the cities along the rail road is 220 miles?

relative speed=2x-10 + x

time to meet: distance/relative speed

= 220/(3x-10)

How far Boston from boston station

distance=speed*time
= x*220/(3x-10)

To solve this problem, we'll need to set up an equation using the given information.

Let's say the speed of the second train is x miles per hour. According to the problem, the speed of the first train is 10 miles per hour less than twice the speed of the second train, which can be written as 2x - 10.

Let's assume that the two trains meet after t hours. In this time, the first train travels a distance of (2x - 10) * t, and the second train travels a distance of x * t.

Since the total distance between Boston and New York is 220 miles, we can set up the equation:

(2x - 10) * t + x * t = 220

Now, let's solve this equation to find the value of t.

Using the distributive property, we can rewrite the equation as:

2xt - 10t + xt = 220

Combining like terms, we get:

3xt - 10t = 220

Factoring out t, we have:

t(3x - 10) = 220

Dividing both sides by (3x - 10), we find:

t = 220 / (3x - 10)

Now, we have the value of t.

To find the distance from the Boston station where they meet, we can substitute the value of t into either of the distance formulas:

Distance traveled by the first train: (2x - 10) * t
Distance traveled by the second train: x * t

Let's substitute the value of t into the distance formula for the first train:

Distance from Boston station = (2x - 10) * t

Now, you can substitute the value of t (which we found earlier) into the equation to calculate the distance.