Two trains leave stations 288 miles apart at the same time and travel toward each other. One train travels at 85 miles per hour while the other travels at 75 miles per hour. How long will it take for the two trains to meet?
Do not do any rounding.
Answer
Final Answer: The two trains will meet after \(\boxed{1.8}\) hours.
Step 1 ：Given that two trains leave stations 288 miles apart at the same time and travel toward each other. One train travels at 85 miles per hour while the other travels at 75 miles per hour.
Step 2 ：The two trains are moving towards each other, so their speeds add up. The total distance to be covered is 288 miles.
Step 3 ：We can find the time it takes for the two trains to meet by dividing the total distance by the combined speed of the two trains. This can be represented by the formula \(time = \frac{distance}{speed1 + speed2}\).
Step 4 ：Substituting the given values into the formula, we get \(time = \frac{288}{85 + 75}\).
Step 5 ：Solving the equation gives \(time = 1.8\) hours.
Step 6 ：Final Answer: The two trains will meet after \(\boxed{1.8}\) hours.
