The speed of a passenger train is 20 mph faster than the speed of a freight train. The passenger train travels 250 miles in the same time it takes the freight train to travel 150 miles. find the speed of each train.
V = slower train speed
V + 20 = faster train speed
T = number of hours required by both
V*T = 150
(V + 20)*T = 250
V*T + 20T = 250
20 T = 100
T = 5 hours
V = 150/T = 30 mph
faster train speed = V + 20 = 50 mph
Let's denote 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 that of the freight train. Therefore, the speed of the passenger train can be expressed as (x + 20) mph.
Now, let's determine the time it takes for each train to travel their respective distances.
For the passenger train, the time taken to travel 250 miles can be represented as 250/(x + 20) hours.
For the freight train, the time taken to travel 150 miles can be represented as 150/x hours.
Since both trains take the same amount of time, we can set up the following equation:
250/(x + 20) = 150/x
To solve this equation, we can cross-multiply:
250x = 150(x + 20)
250x = 150x + 3000
Subtracting 150x from both sides:
100x = 3000
Dividing both sides by 100:
x = 30
Therefore, the speed of the freight train is 30 mph.
To find the speed of the passenger train, we can substitute this back into the equation (x + 20):
Speed of passenger train = 30 + 20 = 50 mph
So, the speed of the passenger train is 50 mph and the speed of the freight train is 30 mph.
To find the speed of each train, we can set up a system of equations based on the given information.
Let's assume the speed of the freight train is x mph.
According to the problem, the speed of the passenger train is then x + 20 mph.
We are given that the passenger train travels 250 miles in the same time it takes the freight train to travel 150 miles.
We can use the formula: Time = Distance / Speed
For the passenger train:
Time = 250 / (x + 20)
For the freight train:
Time = 150 / x
Since the times are equal, we can set up the equation:
250 / (x + 20) = 150 / x
To simplify the equation, we can cross-multiply:
250x = 150(x + 20)
Distribute 150:
250x = 150x + 3000
Subtract 150x from both sides:
100x = 3000
Divide both sides by 100:
x = 30
Therefore, the speed of the freight train is 30 mph.
To find the speed of the passenger train, we can substitute the value of x into the equation:
Speed of passenger train = x + 20
Speed of passenger train = 30 + 20
Speed of passenger train = 50 mph
Hence, the speed of the passenger train is 50 mph and the speed of the freight train is 30 mph.