The speed of train A is 16 mph slower than train B. Train A travels 190 mph in the same time it takes train B to travel 270 miles. Find the speed of each train.
speed of slower train = x mph
speed of faster train = x+16 mph
time for slow train to go 190 miles = 190/x
time for fast train to go 270 miles = 270/(x+16)
but the times are the same ....
190/x = 270/(x+16)
cross-multiply and solve for x, easy from here.
To find the speed of the trains, let's assume that the speed of Train B is "x" mph.
According to the given information, the speed of Train A is 16 mph slower than Train B, which means it would be (x - 16) mph.
We also know that Train A takes the same time as Train B to travel a certain distance.
Using the formula: speed = distance/time, we can set up the following equations:
For Train A: 190 miles = (x - 16) mph * t hours (where t is the time taken in hours)
For Train B: 270 miles = x mph * t hours
Since both trains have the same travel time, we can equate the values of t:
190/(x - 16) = 270/x
Now, let's solve this equation to find the value of x and then calculate the speeds of Train A and Train B.
To solve the equation, first, cross multiply:
190x = 270(x - 16)
Expand the equation:
190x = 270x - 4320
Bring all the "x" terms to the left side and the constants to the right side:
270x - 190x = 4320
Combine like terms:
80x = 4320
Divide both sides by 80:
x = 4320/80
x = 54
So, the speed of Train B is 54 mph.
Now, substitute this value back into one of the original equations to find the speed of Train A:
Speed of Train A = Speed of Train B - 16
Speed of Train A = 54 - 16 = 38 mph
Therefore, the speed of Train A is 38 mph and the speed of Train B is 54 mph.