It takes a passenger train 2 hours less time than it takes a freight train to make the trip from Central City to Clear Creek. The passenger train averages 96mi/hr while the freight train averages 64mi/hr. How far is it from Central City to Clear Creek?
The basic formula is rate x time = distance. Since the freight train and the passenger train are traveling the same distance, the rate x time for each train equals the other. Let t = the time for the freight train. Then t-2 would equal the time for the passenger train, since it took two hours less time to make the trip. Now you have two equations:
passenger train:
r x t = d, 96 x (t-2) = d
freight train:
r x t = d, 64 x t = d
They both equal d, so they equal each other: 96 x (t-2) = 64 x t
Now solve for t and plug in your equation to find d, the distance.
Note: don't forget to distribute the negative sign on 96(t-2).
To find the distance from Central City to Clear Creek, we can use the formula:
Distance = Speed × Time
Let's assume the time taken by the freight train to make the trip is 'T' hours.
Therefore, the time taken by the passenger train would be 'T - 2' hours (as it takes 2 hours less time).
The speed of the passenger train is given as 96 mi/hr, so we can write:
Distance = 96 × (T - 2)
Similarly, the speed of the freight train is given as 64 mi/hr, so we can write:
Distance = 64 × T
Since both expressions represent the same distance, we can set them equal to each other:
96 × (T - 2) = 64 × T
Now we can solve this equation to find the value of T, which represents the time taken by the freight train:
96T - 192 = 64T
Subtracting 64T from both sides gives:
32T - 192 = 0
Adding 192 to both sides gives:
32T = 192
Dividing both sides by 32 gives:
T = 6
So, it takes the freight train 6 hours to make the trip.
To find the distance, we can substitute this value of T back into either equation:
Distance = 64 × T
Distance = 64 × 6
Distance = 384 miles
Therefore, the distance from Central City to Clear Creek is 384 miles.