the speed of train A is 8 mph slower than the speed of train B. Train A travels 220 miles in the same time it takes train B to travel 260 miles. Find the speed of both trains.
Speed of train A =
Speed of train B =
To find the speed of both trains, let's assume the speed of Train B is represented by "x" mph.
According to the given information, the speed of Train A is 8 mph slower than Train B. Therefore, the speed of Train A would be (x - 8) mph.
We are also given that Train A travels 220 miles in the same time it takes Train B to travel 260 miles. This indicates that the time taken by both trains is the same.
Now, we can use the formula:
Speed = Distance / Time
Let's calculate the time taken by both trains:
Time taken by Train A = Distance / Speed of Train A
= 220 / (x - 8) (equation 1)
Time taken by Train B = Distance / Speed of Train B
= 260 / x (equation 2)
Since the time taken by both trains is the same, we can equate equation 1 and equation 2:
220 / (x - 8) = 260 / x
Let's cross-multiply:
220x = 260(x - 8)
220x = 260x - 2080
-40x = -2080
Dividing both sides by -40:
x = -2080 / -40
x = 52
Therefore, the speed of Train B is 52 mph.
To find the speed of Train A, substitute the value of Train B's speed (x) into (x - 8):
Speed of Train A = 52 - 8
= 44 mph
Hence, the speed of Train A is 44 mph and the speed of Train B is 52 mph.