Questions: 2.4 Part 1 of 2 points Points: 0 of 1 Save The sum of the fastest speeds of two trains is 573 miles per hour. If the maximum speed of the first train is 65 mph faster than the maximum speed of the second train, find the speeds of each. What is the speed of the first train?

Solution Steps

To solve this problem, we need to set up a system of equations based on the information given. Let the speed of the second train be \( x \) mph. Then, the speed of the first train is \( x + 65 \) mph. According to the problem, the sum of their speeds is 573 mph. We can set up the equation \( x + (x + 65) = 573 \) and solve for \( x \).

Let the speed of the second train be \( x \) mph. According to the problem, the speed of the first train is \( x + 65 \) mph. The sum of their speeds is given as 573 mph. Therefore, we can set up the equation: \[ x + (x + 65) = 573 \]

Simplify the equation: \[ 2x + 65 = 573 \] Subtract 65 from both sides: \[ 2x = 508 \] Divide both sides by 2 to solve for \( x \): \[ x = 254 \]

The speed of the first train is \( x + 65 \). Substitute the value of \( x \) we found: \[ x + 65 = 254 + 65 = 319 \]

Final Answer