a passenger train is 40 mph faster than a freight train. in the time it takes the slower freight train to travel 161 miles the passenger train can travel 301 miles. What is the speed of each train?
Let's call the speed of the freight train "x" mph.
Therefore, the speed of the passenger train is "x + 40" mph.
We know that the time it takes for the freight train to travel 161 miles is equal to the time it takes for the passenger train to travel 301 miles.
Using the formula "distance = speed * time," we can set up two equations:
For the freight train:
161 = x * t
For the passenger train:
301 = (x + 40) * t
Solving for "t" in the first equation:
t = 161 / x
Substituting t into the second equation:
301 = (x + 40) * (161 / x)
Multiplying both sides by x to eliminate the fraction:
301x = (x + 40) * 161
Expanding the right side:
301x = 161x + 6440
Moving all terms to one side:
301x - 161x = 6440
140x = 6440
Dividing both sides by 140:
x = 6440 / 140
x = 46
So the speed of the freight train is 46 mph.
Substituting this value back into the first equation:
t = 161 / 46
t ≈ 3.5 hours
Therefore, the speed of the passenger train is:
x + 40 = 46 + 40 = 86 mph.
So the speed of the passenger train is 86 mph.