EQUATIONS AND INEQUALITIES Solving a distance, rate, time problem using a linear equation Two trains leave stations 204 miles apart at the same time and travel toward each other. One train travels at 80 miles per hour while the other travels at 90 miles per hour. How long will it take for the two trains to meet? Do not do any rounding. hours

Step 1 ：Two trains leave stations 204 miles apart at the same time and travel toward each other. One train travels at 80 miles per hour while the other travels at 90 miles per hour. We need to find out how long it will take for the two trains to meet.

Step 2 ：The two trains are moving towards each other, so their speeds add up. The total distance to be covered is 204 miles.

Step 3 ：We can set up the equation Distance = Speed * Time, where Speed is the sum of the speeds of the two trains, and Time is the time it takes for the two trains to meet.

Step 4 ：Let's denote the speed of the first train as \(speed_{train1} = 80\) miles per hour, the speed of the second train as \(speed_{train2} = 90\) miles per hour, and the total distance as \(distance = 204\) miles.

Step 5 ：Substituting these values into the equation, we get \(204 = (80 + 90) * time\).

Step 6 ：Solving this equation for time, we get \(time = \frac{204}{80 + 90} = 1.2\) hours.

Step 7 ：Final Answer: The time it will take for the two trains to meet is \(\boxed{1.2}\) hours.