Final answer:
By using the formula distance = speed × time and setting up equations with the given distances, we find that the speed of train B is 55 mph, and the speed of train A, being 25 mph faster, is 80 mph.
Step-by-step explanation:
To solve for the speeds of the two trains, Train A and Train B, we can use the formula distance = speed × time. Here, both trains have traveled for the same amount of time. Since train A is 25 miles per hour faster than train B, if we let the speed of train B be x miles per hour, then the speed of train A will be (x + 25) miles per hour.
Using the given distances that each train travels, we can set up the following equations:
- Speed of train A × time = 240 miles
- Speed of train B × time = 165 miles
This gives us:
- (x + 25) × time = 240
- x × time = 165
Since the time is the same for both trains, we can divide the two equations to get:
(x + 25)/x = 240/165
Cross multiplying and simplifying the equation gives us the value of x:
x = 165 × 25 / (240 - 165)
Calculating this, we find that x = 55 mph. Therefore, the speed of train B is 55 mph, and the speed of train A is 55 + 25 = 80 mph.