Two trains started moving at the same time, train A from Boston to New York, and train B from New York to Boston. The distance between the train stations in New York and Boston is 240 miles. The average speed of train A is 60 mph, which is 3 4 of the average speed of train B.
b
How far from New York will the trains meet?

102.6 miles

Step-by-step explanation:

In this problem, the initial distance between the two trains is the distance between New York and Boston, so

d = 240 miles

We know that the average speed of train A is 60 mph, and that train A travels from Boston to New York, so we can write its velocity as

At the same time, train B travels from New York to Boston, so its velocity will be negative (since it is going in the opposite direction).

Also, we know that the speed of train B is 3/4 that of train A, so we have:

So, velocity of train B is 45 mph towards Boston.

Taking Boston as zero position as reference, x = 0, the position of train A at time t can be written as

While the position of train B at time t is

The two trains meet when they have same position, so when

And so when

Solving for t,

The position at which they meet is

However, this is the distance from Boston; so the distance from New York is:

congruent segments

step-by-step explanation: