the speed of a passenger train is 18mph faster than the speed of a freight train. The passenger train travels 310 miles in the same time it takes the freight train to travel 220 miles. Find the speed of each train passenger train mph and freight train mph

time= distance/speed

Because the time used to travel is the same (regardless of the difference in distance) we can set the freight trains time equal to the passenger train's time.
Let's start off with the freight train. The distance is 310. It says the speed is 18 mph faster than the speed of the freight train. So I pets set a variable: X, where X is the speed of the freight train. Therefore the time if the freight train, distance over time, can be substituted with 310mph/X+18

now the time of the freight train. The distance is 220, and the speed is X. Therefore, the time is distance over speed, which you can subatitute into 220/X

Now, set the time equal.

319/X+18 = 220/X
Solve for x, and you'll find the freight train is 44 mph, and the pass train is 62 mph.

Cheers!😀😀😀😀😀😀😀😀😀

To solve this problem, we can create two equations based on the given information and then solve them simultaneously.

Let's assume the speed of the freight train is denoted by 'x' mph.

According to the problem, the speed of the passenger train is 18 mph faster than the freight train. Therefore, the speed of the passenger train can be represented as 'x + 18' mph.

We are given that the passenger train travels 310 miles in the same amount of time it takes the freight train to travel 220 miles. We can use the formula: time = distance / speed.

For the passenger train:
Time = 310 miles / (x + 18) mph

For the freight train:
Time = 220 miles / x mph

Since both trains take the same time to travel their respective distances, we can set these two equations equal to each other:

310 / (x + 18) = 220 / x

To simplify the equation, we can cross-multiply:
310x = 220(x + 18)

Expanding the equation:
310x = 220x + 3960

Subtracting 220x from both sides:
90x = 3960

Now, divide both sides by 90:
x = 44

So, the speed of the freight train is 44 mph.

To find the speed of the passenger train, we can substitute the value of x back into one of the equations:

Passenger train speed = x + 18 = 44 + 18 = 62 mph

Therefore, the speed of the passenger train is 62 mph and the speed of the freight train is 44 mph.