Two trains leave stations 532 miles apart at the same time and travel toward each other. One train travels at 85 miles per hour while the other travels at 105 miles per hour. How long will it take for the two trains to meet?
Do not do any rounding.
Let's call the distance between the two trains "x". At the beginning, x = 532 miles. As the trains move towards each other, the distance between them decreases. We want to find out how long it will take for that distance to reach 0 (i.e. for the trains to meet).
We can set up an equation using the formula d = rt, where d is distance, r is rate (in this case, the speed of the trains), and t is time. For one train,
d = rt
d = 85t
For the other train,
d = rt
d = 105t
Since both trains are moving towards each other, we can add up their distances:
d1 + d2 = 532
85t + 105t = 532
Simplifying, we get:
190t = 532
Dividing both sides by 190, we get:
t = 532/190
This fraction cannot be simplified any further, so our final answer is:
t = 2.8 hours
It will take 2.8 hours (or 2 hours and 48 minutes) for the two trains to meet.
To find the time it takes for the two trains to meet, we can use the formula:
Time = Distance / Relative Speed
Let's calculate the relative speed of the two trains first. Since they are traveling towards each other, we can add their speeds together:
Relative Speed = Speed of Train A + Speed of Train B
= 85 mph + 105 mph
= 190 mph
Now, we substitute the distance and relative speed into the formula:
Time = 532 miles / 190 mph
Dividing the distance by the relative speed gives us:
Time = 2.8 hours
Therefore, it will take 2.8 hours for the two trains to meet.