the speed of train A is 14 miles slower than train B. train A travels 210 miles in the same time it takes train B to travel 280 miles. Whats the speed of each train?
8A = 7B
A + 14 = B
8A = 7(A+14) =
8a = 7A + 7*14
A = 7*14
A = 7*7*2 = 49*2 = 98 mph
B = 98+14 = 112
To solve this problem, let's set up some equations.
Let the speed of train A be represented by "x" miles per hour.
Since train A is 14 miles slower than train B, the speed of train B will be represented as "x + 14" miles per hour.
Now, we know that the time it takes for train A to travel 210 miles is the same as the time it takes for train B to travel 280 miles.
We can use the formula: time = distance / speed
For train A, the time taken will be 210 miles / x miles per hour.
For train B, the time taken will be 280 miles / (x + 14) miles per hour.
Since both times are equal, we can set up the equation:
210 / x = 280 / (x + 14)
Now, let's solve for x.
First, cross-multiply to get rid of the fractions:
210 * (x + 14) = 280 * x
Multiply on both sides and simplify:
210x + 2940 = 280x
Subtract 210x from both sides:
2940 = 70x
Divide both sides by 70:
x = 42
So, the speed of train A is 42 miles per hour.
Now, to find the speed of train B, we can substitute the value we found for x:
Speed of train B = 42 + 14 = 56 miles per hour.
Therefore, the speed of train A is 42 mph, and the speed of train B is 56 mph.