Final answer:
To meet at 10:12 AM, Tom and Mark must travel at 17.5 km/h and 22.5 km/h, respectively, towards each other from towns 45 km apart.
Step-by-step explanation:
To solve the problem of when Mark and Tom will meet, we need to set up an equation based on their rates of travel and the time they take. They are starting 45 km apart and want to meet at 10:12 AM, which is 1 hour and 12 minutes, or 1.2 hours, after they started at 9:00 AM.
Let's assume Tom's speed is x km/h. Then Mark's speed would be x + 5 km/h. Since they are moving towards each other, their combined rate is x + (x + 5) or 2x + 5 km/h. In 1.2 hours, the distance they will cover together is (2x + 5) * 1.2 km.
To find the speeds at which they must travel, we set up the equation (2x + 5) * 1.2 = 45, which can be solved to find the value of x, Tom's speed, and thereby Mark's speed. After solving, we find that Tom must travel at 17.5 km/h and Mark at 22.5 km/h to meet at 10:12 AM.