Speed of passenger train is 6mph faster than the freight train. The passenger train travels 260 miles at the same time the freight train travels 230 mph. WHAT would be the speed of both the passenger and freight trains?????
speed of freight --- x mph
speed of passenger --- x+6 mph
time to go 230 by freight = 230/x
time to go 260 by pass = 260/(x+6)
but they are equal, so
230/x = 260/(x+6)
260x = 230x + 1380
30x = 1380
x = 46
speed of freight is 46 mph , and the passenger train is 52 mph
check: 230/52 = 1/5 hrs
230/46 = 1/5 hr
all is good
To find the speeds of both the passenger and freight trains, 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 given information, the speed of the passenger train is 6 mph faster than the freight train. So, the speed of the passenger train would be "x + 6" mph.
The distance traveled by the passenger train is 260 miles, and to cover this distance, it takes the same time as the freight train traveling at 230 mph over a distance of 230 miles.
Using the formula: Speed = Distance / Time, we can set up the following equations:
For the passenger train: (x + 6) mph = 260 miles / Time
For the freight train: x mph = 230 miles / Time
Since both trains took the same amount of time to travel their respective distances, we can assume that the Time is the same in both equations.
To solve this system of equations, we can equate the two expressions for Time:
260 miles / (x + 6) mph = 230 miles / x mph
Next, we can cross multiply:
260x = 230(x + 6)
260x = 230x + 1380
Now, simplify the equation:
260x - 230x = 1380
30x = 1380
Divide both sides of the equation by 30:
x = 1380 / 30 = 46
So, the speed of the freight train is 46 mph.
To find the speed of the passenger train, we can substitute the value of x into the equation for the passenger train's speed:
Passenger train speed = 46 + 6 = 52 mph
Therefore, the speed of the passenger train is 52 mph, and the speed of the freight train is 46 mph.