The The speed of a passenger train is 12 mph faster then the speed of a freight train. The passenger train travels 270 miles in the same time it takes the freight train to travel 210 miles. Find the speed of each train.
Let the speed of the freight train be x mph
then the speed of the passenger train is x+12 mph
Time for freight train = 210/x
time for passenger train = 270/(x+12)
but they are equal so....
270/(x+12) = 210/x
cross-multiply and solve.
Let me know what you got.
If we take the speed of the freight train to be x, and the speed of the passenger train to be y, we get that:
1)y=x+12
2)270/y=210/x
So if we replace y in the second equation by the y we found in the forst equation, we get that:
270/(x+12)=210/x
=>210*(x+12)=270x
=>60x=2520
=>x=42
=>y=54
So the freight train moves at 42mph and the passenger train moves at 54mph
The speed of a passenger train is 18 mph 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.
To solve this problem, we can create a system of equations based on the given information.
Let's denote the speed of the freight train as "x" mph.
According to the problem, the speed of the passenger train is 12 mph faster than the speed of the freight train. Therefore, the speed of the passenger train would be "x + 12" mph.
The time taken by both trains to travel their respective distances is the same. We can use the formula: Time = Distance / Speed.
For the freight train, the time it takes to travel 210 miles is given by:
Time = 210 / x.
For the passenger train, the time it takes to travel 270 miles is given by:
Time = 270 / (x + 12).
Since both trains take the same amount of time to travel their respective distances, we can set up the equation:
210 / x = 270 / (x + 12).
Now, we can solve the equation to find the value of x, which represents the speed of the freight train:
Cross-multiplying the equation, we have:
210(x + 12) = 270(x).
Expanding both sides of the equation:
210x + 2520 = 270x.
Rearranging the equation by moving all the terms to one side:
270x - 210x = 2520.
Combining like terms:
60x = 2520.
Dividing both sides by 60:
x = 42.
Therefore, the speed of the freight train is 42 mph.
To find the speed of the passenger train, we can substitute this value back into the equation:
Speed of the passenger train = x + 12 = 42 + 12 = 54 mph.
Thus, the speed of the passenger train is 54 mph and the speed of the freight train is 42 mph.