the speed of a passenger train is 6 mph faster than the speed of a freight train. The passenger train travels 330 miles in the same time it takes the freight train to travel 300 miles.Find the speed of each train.

speed of freigh --- x

speed of passenger ---- x+6

time for passenger to go 330 miles = 330/(x+6) hrs
time for freight train to go 300 miles = 300/x hrs
but the times are the same

330/(x+6) = 300/x
330x = 300x + 1800
30x = 1800
x = 60

state the conclusion

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

According to the given information, the speed of the passenger train is 6 mph faster, so the speed of the passenger train is (x + 6) mph.

Now, we know that time = distance / speed.

For the passenger train: time = 330 miles / (x + 6) mph.

For the freight train: time = 300 miles / x mph.

Since the time taken by both trains is the same, we can equate the expressions:

330/(x + 6) = 300/x.

To solve this equation, we can cross-multiply:

330x = 300(x + 6).

330x = 300x + 1800.

330x - 300x = 1800.

30x = 1800.

Dividing both sides of the equation by 30:

x = 1800/30.

x = 60.

Therefore, the speed of the freight train is 60 mph.

The speed of the passenger train is (x + 6) = 60 + 6 = 66 mph.

Hence, the speed of the freight train is 60 mph, and the speed of the passenger train is 66 mph.

To find the speed of each train, let's first assign variables to represent their speeds. Let:

x = speed of the freight train (in mph)
x + 6 = speed of the passenger train (in mph)

We are given that the passenger train travels 330 miles in the same time it takes the freight train to travel 300 miles. We can use the formula: Time = Distance / Speed.
For the passenger train:
Time = 330 miles / (x + 6) mph

For the freight train:
Time = 300 miles / x mph

Since the times are equal, we can set up the following equation:
330 / (x + 6) = 300 / x

To solve this equation, we can cross-multiply:
330x = 300(x + 6)
330x = 300x + 1800

Now, let's isolate the x term:
330x - 300x = 1800
30x = 1800

Divide both sides by 30:
x = 60

Therefore, the speed of the freight train is 60 mph.

To find the speed of the passenger train, we substitute this value back into one of our earlier equations:
Speed of passenger train = Speed of freight train + 6
Speed of passenger train = 60 mph + 6 mph
Speed of passenger train = 66 mph

Hence, the speed of the passenger train is 66 mph and the speed of the freight train is 60 mph.