Train A has a speed 20 miles per hour greater than that of train B. If train A travels 270 miles in the same times train B travels 230 miles, what are the speeds of the two trains?
I would let x = speed of train B
and x + 20 = speed of train A
You know the times are equal for the two trains so distance = rate x time or
time = distance/rate
[270/(x+20)] = (230/x)
Solve for x and x + 20.
To solve this problem, we need to set up an equation using the given information.
Let's assume the speed of train B is x miles per hour.
According to the problem, the speed of train A is 20 miles per hour greater than that of train B. So, the speed of train A is (x + 20) miles per hour.
The time taken by both trains is the same. We can use the formula:
Time = Distance / Speed
For train B, the time taken to travel 230 miles is given by:
Time_B = 230 / x
For train A, the time taken to travel 270 miles is given by:
Time_A = 270 / (x + 20)
Since the times are equal, we can set up the equation:
230 / x = 270 / (x + 20)
Now, let's solve this equation to find the speed of train B (x) and then calculate the speed of train A.
First, we cross multiply the equation:
230 * (x + 20) = 270 * x
230x + 4600 = 270x
4600 = 270x - 230x
4600 = 40x
Now, we can divide both sides of the equation by 40 to isolate x:
4600 / 40 = x
115 = x
So, the speed of train B is 115 miles per hour.
To find the speed of train A, we can substitute this value back into one of the equations. Let's use the equation:
Speed_A = x + 20
Speed_A = 115 + 20
Speed_A = 135 miles per hour.
Therefore, the speed of train B is 115 miles per hour, and the speed of train A is 135 miles per hour.