The speed of train A is 6 mph slower than the speed of train B. Train A travels 200 miles in the same time it takes train B to travel 230 miles. Find the speed of speed of each train.
Train B travels X mi/h.
Train A travels (x-6) mi/h.
X*t/(x-6)t = 230/200, X/(x-6) = 230/200, 200x = 230x-1380, -30x = -1380, X = 46 mi/h, x-6 = 46-6 = 40 mi/h.
To find the speeds of trains A and B, let's break down the problem and create equations based on the given information.
Let's say the speed of train B is "x" mph. According to the problem, the speed of train A is 6 mph slower than train B, so the speed of train A is "x - 6" mph.
The time taken for both trains to travel their respective distances is the same. Therefore, we can set up an equation based on the formula "Distance = Speed * Time" for both trains.
For train A:
Distance = 200 miles
Speed = x - 6 mph
Time = Distance / Speed = 200 / (x - 6)
For train B:
Distance = 230 miles
Speed = x mph
Time = Distance / Speed = 230 / x
Since the time taken by both trains is the same, we can set up an equation by equating the two Time values:
200 / (x - 6) = 230 / x
To solve this equation for x, we can cross-multiply:
200x = 230(x - 6)
Expanding the equation:
200x = 230x - 1380
Bringing like terms to one side gives:
230x - 200x = 1380
30x = 1380
Dividing both sides by 30:
x = 46
Therefore, the speed of train B is 46 mph.
Since train A is 6 mph slower than train B, the speed of train A is:
x - 6 = 46 - 6 = 40 mph.
So, train A has a speed of 40 mph and train B has a speed of 46 mph.