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.
If train B's speed is x, then A's is x-6
Since time = distance/speed,
200/(x-6) = 230/x
To find the speeds of trains A and B, let's set up an equation based on the given information.
Let the speed of train B be "x" mph. Since train A is 6 mph slower, the speed of train A would be "x - 6" mph.
Next, we'll determine the time it takes for each train to travel their respective distances. We can use the formula: Time = Distance / Speed.
For train A: Time taken = 200 / (x - 6)
For train B: Time taken = 230 / x
According to the problem, train A takes the same time as train B. This forms the equation:
200 / (x - 6) = 230 / x
Now, we can solve this equation to find the value of "x", which represents the speed of train B.
To simplify the equation, we can cross-multiply:
200x = 230(x - 6)
Expanding the equation:
200x = 230x - 1380
Subtracting 230x from both sides:
200x - 230x = -1380
Combining like terms:
-30x = -1380
Dividing both sides by -30:
x = (-1380) / (-30)
x = 46
Therefore, the speed of train B is 46 mph.
Now, we can find the speed of train A by substituting the value of x back into the expression "x - 6":
Speed of train A = 46 - 6
Speed of train A = 40 mph
Thus, the speed of train A is 40 mph, and the speed of train B is 46 mph.