The speed of a passenger train is 16 mph faster than the speed

of a freight train. The passenger train travles 300 miles in
the same time it takes the freight train to travel 220 miles.
find the speed of each train

Let's assume the speed of the freight train is x mph. Then, the speed of the passenger train would be x + 16 mph.

We know that the time taken is the same for both trains. Distance divided by speed gives us time.

For the passenger train:
Time = Distance/Speed
Time = 300 miles / (x + 16) mph

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

Since the time taken is the same, we can set these two equations equal to each other:
300 / (x + 16) = 220 / x

To solve for x, we can cross multiply:
300x = 220(x + 16)

Expanding the equation:
300x = 220x + 3520

Subtracting 220x from both sides:
80x = 3520

Dividing by 80 on both sides to solve for x:
x = 44

Therefore, the speed of the freight train is 44 mph, and the speed of the passenger train would be 44 + 16 = 60 mph.

To find the speed of each train, we can set up a system of equations based on the given information. Let's assume that the speed of the freight train is "x" miles per hour (mph).

According to the problem, the speed of the passenger train is 16 mph faster than the speed of the freight train. Therefore, the speed of the passenger train is "x + 16" mph.

Next, we need to determine the time it takes for each train to travel their respective distances. We know that time equals distance divided by speed.

For the passenger train, the distance is 300 miles and the speed is "x + 16" mph. So, the time taken by the passenger train can be expressed as 300/(x + 16).

For the freight train, the distance is 220 miles and the speed is "x" mph. So, the time taken by the freight train can be expressed as 220/x.

Since both trains take the same time to travel their respective distances, we can set up an equation:

300/(x + 16) = 220/x

Now, we need to solve this equation to find the value of "x" (the speed of the freight train). Let's multiply both sides of the equation by (x)(x + 16) to eliminate the denominators:

300x = 220(x + 16)

Expanding the equation:

300x = 220x + 3520

Simplifying:

300x - 220x = 3520

80x = 3520

Dividing both sides of the equation by 80:

x = 44

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

To find the speed of the passenger train, we can substitute this value back into the equation for the passenger train's speed:

Passenger train speed = x + 16 = 44 + 16 = 60 mph.

Thus, the speed of the passenger train is 60 mph and the speed of the freight train is 44 mph.

speed of freight --- x mph

speed of passenger --- x+16 mph

freight can go 220 miles in 220/x hours
pass. can go 300 miles in 300/(x+16) hrs

but those times are the same ....
220/x = 300/(x+16)
cross-multiply
300x = 220x + 3520
80x = 3520
x = 44

the freight goes 44 mph and the passenger train goes 60 mph