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.