Two trains leave stations 288 miles apart at the same time and travel toward each other. One train travels at 95 miles per hour while the other travels at 85 miles per hour. How long will it take for the two trains to meet?
Do not do any rounding.
To find the time it takes for the two trains to meet, we can use the formula:
\[\text{{Distance}} = \text{{Speed}} \times \text{{Time}}.\]
Let's assume that the time it takes for the trains to meet is \(t\) hours.
The train traveling at 95 miles per hour travels \(95t\) miles in \(t\) hours, and the train traveling at 85 miles per hour travels \(85t\) miles in \(t\) hours.
Since the two trains travel towards each other, the sum of the distances they have traveled is equal to the total distance between the two stations, which is 288 miles.
So, we can write the equation:
\(95t + 85t = 288\).
Combining like terms, we get:
\(180t = 288\).
Dividing both sides of the equation by 180, we find:
\(t = \frac{288}{180} = \frac{16}{10} = \frac{8}{5} = 1.6\).
Therefore, it will take the two trains 1.6 hours to meet.