Final answer:
Tom and Dom will cross each other 100 miles away from City A. The problem is solved by calculating the distance Dom covers before Tom starts, then using their combined speeds to determine when they meet.
Step-by-step explanation:
To solve this problem, we'll calculate how long Dom has been traveling before Tom starts his journey and how far Dom will travel in that time. Then, we'll determine the combined average speed of both Tom and Dom when they are moving towards each other and use this to find the distance at which they cross each other.
Firstly, since Tom leaves 20 minutes after Dom, we'll convert those minutes into hours because the speed is given in miles per hour (mph). 20 minutes is equal to 20/60 hours, which is 1/3 hour or approximately 0.333 hours. In this time, Dom, driving at 60 mph, would have covered a distance of 60 mph × 0.333 hours = 20 miles. Therefore, when Tom starts driving, the remaining distance between them is 240 miles - 20 miles = 220 miles.
Now, to find the time it takes for them to meet, we can use the combined speed of both vehicles. The combined speed is 60 mph + 50 mph = 110 mph. The time it takes for them to meet is the remaining distance divided by their combined speed, so:
Time = Distance ÷ Combined Speed = 220 miles ÷ 110 mph = 2 hours.
Tom travels for 2 hours at 50 mph, so the distance Tom covers before they meet is 50 mph × 2 hours = 100 miles. Hence, they will cross each other 100 miles away from City A.