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.
Train A is 23/29 as fast as train B.
Va/Vb = 23/29
Va = Vb -12
(23/29)Vb -Vb = -12
(6/29)Vb = 12
Vb = 58 mph
Va = 46 mph
To find the speed of each train, we can set up a system of equations based on the given information.
Let's assume the speed of Train A is x mph and the speed of Train B is y mph.
According to the given information, Train A is 12 mph slower than Train B. So we can write the first equation as:
x = y - 12 ...(Equation 1)
Also, Train A travels 230 miles in the same time it takes Train B to travel 290 miles. The time it takes for both trains to travel a certain distance is given by the formula:
time = distance / speed
For Train A, the time is 230 miles divided by its speed, which is x mph. So, the second equation is:
230/x = 290/y ...(Equation 2)
We now have a system of two equations (Equation 1 and Equation 2). We can solve this system to find the values of x and y.
To solve the system, we can rearrange Equation 1 to express y in terms of x:
y = x + 12 ...(Equation 3)
Now, substitute Equation 3 into Equation 2:
230/x = 290/(x + 12)
To solve this equation, first, cross-multiply to get:
230(x + 12) = 290x
Expand the brackets:
230x + 2760 = 290x
Now, move all x terms to one side and the constant terms to the other side:
290x - 230x = 2760
60x = 2760
Divide both sides by 60:
x = 46
Now, substitute the value of x into Equation 3 to find y:
y = 46 + 12
y = 58
Therefore, the speed of Train A is 46 mph and the speed of Train B is 58 mph.