To solve, refer to the figure.

Let d1 be the distance traveled by the first car and d2 be the distance traveled by the second car.

Since the two cars are 150 miles apart at the start, when they meet, the sum of their distances traveled is 150 miles.

`d_1+d_2=150`

Then, express the equation in terms of time. Let t be the number of hours that the cars been traveling. The two cars have the same variable t since they start at the same time. Applying the formula

distance =speed *time

the distance traveled by each car expressed in t are

`45t + 55t = 150`

The left side simplifies to

`100t=150`

Dividing both sides by 100, it becomes

`(100t)/105=150/100`

`t=1.5`

So the value of t is 1.5 hours.  To get the time, express the value of t in hours and minutes. To do so, convert the decimal part to minutes.

`t = 1 hr + 0.5 hr`

`t = 1 hr + 0.5 h * (60 min)/(1hr)`

`t = 1 hr + 30 min`

It is after 1 hour and 30 minutes that the two cars will meet. Since the cars left at 2:15, therefore, they will pass each other at 3:45.