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?

Question

Do not do any rounding.

Answer 1

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.