A freight train travels 260 km in the same time a passenger train travels 320 km. If the passenger train averages 15km/hour faster than the freight train, what is the average speed of the freight?
time = t
vf t = 260
vp t = 320
so
260/vf = 320/(vf+15)
320 vf = 260 vf +260(15)
60 vf = 390
3 vf = 39
vf = 13 km/hour
To find the average speed of the freight train, we first need to determine the time it takes for each train to travel their respective distances.
Let's assume the average speed of the freight train is "x" km/h.
The passenger train, which is traveling 15 km/h faster, will have an average speed of "x + 15" km/h.
We can use the formula: time = distance / speed, where time is in hours, distance is in km, and speed is in km/h.
For the freight train:
time = 260 km / x km/h
For the passenger train:
time = 320 km / (x + 15) km/h
Since both trains travel for the same time:
260 / x = 320 / (x + 15)
To solve this equation, we can cross multiply:
260(x + 15) = 320x
Now, let's solve for x:
260x + 3900 = 320x
Bringing "320x" to the left side, we have:
320x - 260x = 3900
60x = 3900
Dividing both sides by 60:
x = 65
Therefore, the average speed of the freight train is 65 km/h.