Two trains leave the station at the same time, one heading east and the other west. The eastbound train travels at 80 miles per hour. The westbound train travels at 90 miles per hour. How long will it take for the two trains to be 374 miles apart?
Do not do any rounding.
Let's call the time it takes for the trains to be 374 miles apart "t".
During that time, the eastbound train will have traveled 80t miles and the westbound train will have traveled 90t miles.
To find the total distance between the two trains, we can add the distances they have traveled:
Distance = 80t + 90t
Distance = 170t
We know that this distance is equal to 374 miles:
170t = 374
To solve for "t", we can divide both sides by 170:
t = 2.2
So it will take 2.2 hours (or 2 hours and 12 minutes) for the two trains to be 374 miles apart.
To find the time it takes for the two trains to be 374 miles apart, we need to calculate the relative speed of the trains first.
Let's assume that the time taken by both trains is t.
The distance covered by the eastbound train in time t is given by:
Distance = Speed * Time
Distance = 80 * t
Similarly, the distance covered by the westbound train in time t is given by:
Distance = Speed * Time
Distance = 90 * t
Since the two trains are moving in opposite directions, the total distance covered by both trains is the sum of their distances:
Total Distance = 80 * t + 90 * t
Now, we can solve the equation:
Total Distance = 374
80t + 90t = 374
170t = 374
t = 374/170
t = 2.2
Therefore, it will take approximately 2.2 hours for the two trains to be 374 miles apart.