Final answer:
Train B has a speed of 35 mph, and Train A travels at a speed of 52 mph. This is determined by setting the speed of Train B as 'x', establishing an equation to represent the total distance covered by both trains, and solving for 'x'.
Step-by-step explanation:
Two trains start from the same location and travel in opposite directions. To find the speed of each train, let's denote the speed of Train B as 'x' mph. Since Train A is traveling 17 mph faster than Train B, the speed of Train A is therefore 'x + 17' mph.
After traveling for five hours, the trains are 435 miles apart. This means the distance covered by both trains together is 435 miles. We can write the equation:
5x + 5(x + 17) = 435
Expanding and solving for 'x' gives us:
5x + 5x + 85 = 435
10x = 435 - 85
10x = 350
x = 35
Thus, the speed of Train B is 35 mph and the speed of Train A is 35 mph + 17 mph = 52 mph.