two trains are at stations that are 800 miles apart. if they start traveling toward each other at the same time one averaging 67 mph and the other averaging 53 mph in how many hours will they pass each other?

Let's hope they are on separate tracks.

let distance covered by faster train be x miles
then distance covered by slower train is 800-x

When they pass each other, their times must be the same, so ...
x/67 = (800-x)/53
53x = 53600 - 67x
120x = 53600
x = 446 2/3 miles

time = 446 2/3 / 67 = 6 2/3 hours or 6 hrs and 40 minutes

To find out how many hours it will take for the two trains to pass each other, we can use the formula:

Time = Distance / Speed

In this case, the distance between the two stations is 800 miles, and the two trains are moving towards each other. Therefore, the effective distance they need to cover is the sum of their individual distances before they meet.

Let's first calculate the distance covered by the train moving at 67 mph:
Distance1 = Speed1 * Time
Distance1 = 67 mph * Time

Similarly, let's calculate the distance covered by the train moving at 53 mph:
Distance2 = Speed2 * Time
Distance2 = 53 mph * Time

Since the total distance covered by both trains is equal to 800 miles, we can write the equation:
Distance1 + Distance2 = 800

Now substitute the expressions for Distance1 and Distance2:
67 mph * Time + 53 mph * Time = 800

Combining like terms, we get:
120 mph * Time = 800

To isolate Time, divide both sides of the equation by 120 mph:
Time = 800 miles / 120 mph

Simplifying the equation:
Time = 6.67 hours

Therefore, it will take approximately 6.67 hours (or 6 hours and 40 minutes) for the two trains to pass each other.