Final answer:
To determine the speeds of the trains, we set up an equation using their combined distance covered and the initial distance separating them. Solving the equation, we found that the slower train's speed is 80 mph, while the faster train's speed is 90 mph.
Step-by-step explanation:
To solve the problem, we will use the concept of relative speed when two objects move towards each other. The sum of their individual speeds will be equal to the reduced distance they need to cover due to their motion. Let's assume the speed of the slower train is x mph. Therefore, the speed of the faster train is x + 10 mph. In 5 hours, the trains cover distances of 5x and 5(x + 10) miles, respectively.
- The initial distance between the two trains is 1020 miles.
- In 5 hours, they are 170 miles apart.
- So, in 5 hours, they have covered 1020 - 170 = 850 miles together.
Add the distances covered by both trains to get a single equation: 5x + 5(x + 10) = 850
Simplifying,
- 5x + 5x + 50 = 850
- 10x + 50 = 850
- 10x = 800
- x = 80
Thus, the speed of the slower train is 80 mph, and the speed of the faster train is x + 10 which is 90 mph.