the speed of a passenger train is 20mph faster than the speed of a freight train. the passenger train travels 300 miles in the same time it takes the freight train to travel 200miles find the speed of each train.

P-20=F

timefreight= distance/rate=200/F
timepassenger= 300/P

but 300/P=200/F
200P=300F
200P=300(P-20)
solve for P, the speed of the passenger train,then solve for F

To find the speed of each train, let's represent the speed of the freight train as "x" mph.

According to the given information, the speed of the passenger train is 20 mph faster than the speed of the freight train. So, the speed of the passenger train can be represented as "x + 20" mph.

Next, let's determine the time it takes for each train to travel their respective distances.

The time can be calculated using the formula: time = distance / speed.

For the passenger train, the time taken to travel 300 miles is given as the same time taken by the freight train to travel 200 miles. This can be expressed as follows:

300 / (x + 20) = 200 / x

Now we can solve this equation to find the value of "x."

To do this, we can cross-multiply:

300x = 200(x + 20)

Expanding the equation:

300x = 200x + 4000

Subtracting 200x from both sides:

100x = 4000

Dividing both sides by 100:

x = 40

Therefore, the speed of the freight train is 40 mph.

To find the speed of the passenger train, we can substitute the value of x into the equation "x + 20":

40 + 20 = 60

Thus, the speed of the passenger train is 60 mph.

Therefore, the speed of the freight train is 40 mph, and the speed of the passenger train is 60 mph.