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
Let's assume the speed of the slower freight train is 'x' mph.
According to the given information, the speed of the passenger train is 40 mph faster than the freight train. Therefore, the speed of the passenger train can be represented as (x + 40) mph.
The time taken by the slower freight train to travel a distance of 161 miles can be calculated using the formula:
Time = Distance/Speed
Therefore, the time taken by the slower freight train is 161/x.
Similarly, the time taken by the passenger train to travel a distance of 301 miles can be calculated using the formula:
Time = Distance/Speed
Therefore, the time taken by the passenger train is 301/(x + 40).
According to the problem statement, the slower freight train takes the same amount of time as the passenger train to travel their respective distances. Therefore, we can equate the times:
161/x = 301/(x + 40)
To solve this equation, we can cross-multiply:
161(x + 40) = 301x
161x + 6440 = 301x
Subtracting 161x from both sides of the equation:
6440 = 301x - 161x
Combining like terms:
6440 = 140x
Dividing both sides by 140:
x ≈ 45.94
Therefore, the speed of the slower freight train is approximately 45.94 mph.
Since the passenger train is 40 mph faster, the speed of the passenger train is approximately 45.94 + 40 = 85.94 mph.