Two trains leave the station at the same time, one heading east and the other west. The eastbound train travels at 70 miles per hour.
The westbound train travels at 80 miles per hour. How long will it take for the two trains to be 270 miles apart?
Do not do any rounding.
To find the time it takes for the two trains to be 270 miles apart, we can use the formula: distance = rate × time.
Let's assume the time it takes for the trains to be 270 miles apart is t hours.
Since the eastbound train is traveling at 70 miles per hour, its distance can be calculated as 70t.
Similarly, since the westbound train is traveling at 80 miles per hour, its distance can be calculated as 80t.
According to the problem, the sum of the distances traveled by both trains will equal the total distance between them, which is 270 miles.
So, the equation can be written as:
70t + 80t = 270
Simplifying the equation:
150t = 270
Dividing both sides of the equation by 150:
t = 270/150
t = 1.8
Therefore, it will take 1.8 hours, or 1 hour and 48 minutes, for the two trains to be 270 miles apart.