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.
Therefore, the rate of first person is 6.5 miles per hour and rate of second person 3.5 miles per hour.