Train A is 12 mph slower than train B. Train A travels 230
miles in the same time it takes train B to travel 290 miles.
Find the speed of each train.
To solve this problem, let's create variables to represent the speeds of Train A and Train B. Let's call the speed of Train B "x" mph. Since Train A is 12 mph slower than Train B, the speed of Train A will be "x - 12" mph.
Now, we can use the formula: time = distance / speed.
According to the problem, Train A travels 230 miles in the same time it takes Train B to travel 290 miles. So, we can set up the following equation:
230 / (x - 12) = 290 / x
To solve the equation, we can cross-multiply:
230x = 290(x - 12)
Now, let's distribute the 290 to x and -12:
230x = 290x - 3,480
Next, let's subtract 230x from both sides of the equation to isolate the variable:
-60x = -3,480
Dividing both sides of the equation by -60:
x = 58
So, the speed of Train B, which we represented as "x", is 58 mph.
To find the speed of Train A, which is 12 mph slower than Train B, we subtract 12 from the speed of Train B:
58 - 12 = 46
Therefore, Train A travels at a speed of 46 mph and Train B travels at a speed of 58 mph.