Two people begin traveling at the same time from opposite ends of a 20 mile trail. one person travels 3 miles per hour faster than the other. if they meet after 2 hours, what are the rates of the 2 people

Let  us assume rate of other person = x miles per hour.

Rate of first person is 3 miles per hours faster than other.

Therefore, rate of first person = (x+3) miles per hour.

Total distance between them = 20 miles.

And total time taken by them is 2 hours.

We know, distance, time and rate relation:

Distance = Rate × Time.

Therefore, distance covered by other person = x * 2 = 2x.

Distnace covered by first person = (x+3)*2.

Total distance covered by both = 20 miles.

We can setup an equation

Total distance covered by both  = Distnace covered by first person + distance covered by other person.

2(x+3) +2x = 20.

Now, we can solve the eqation for x.

2x +6 +2x = 20.

4x +6 =20.

Subtracting 6 from both sides, we get

4x +6-6 =20-6

4x = 14.

Dividing both sides by 4, we get

x=3.5

Rate of first person = (x+3) = 3.5+3 = 6.5 miles per hour.