Final answer:
The correct equation for two trains headed toward each other from a distance of 420 miles, with Train A traveling at 40 mi/hr and Train B at 30 mi/hr, is A) 40x + 30x = 420. By solving the equation, we find that it takes 6 hours for the trains to meet.
Step-by-step explanation:
The correct equation that represents the scenario where two trains are 420 miles apart and headed toward each other with Train A traveling at 40 mi/hr and Train B at 30 mi/hr is A) 40x + 30x = 420. To find the time (x) before they meet, we set up an equation that adds the distances each train will cover in that time. Since distance is equal to rate multiplied by time (d = rt), Train A's distance is 40x miles and Train B's distance is 30x miles. The sum of these distances should equal the total distance between the trains, which is 420 miles.
To solve for the time (x), we simply add the distances covered by both trains and set the equation equal to 420. This gives us: 40x + 30x = 420. Combining like terms, we get 70x = 420. Dividing both sides by 70, we find x = 6, so it takes 6 hours for the trains to meet.