two boats are traveling towards the same ports from opposite directions. they are 63 miles apart and one boat is traveling 6 mph faster than the other. if the Boats both reach the port in 4 hours and 30 minutes, find the speed for each.

distance (d) = rate (r) x time (t)

Time Rate Distance Equation

Boat 1: 4.5 hrs x y 4.5x = y

Boat 2: 4.5 hrs x + 6 63 - y 4.5 (x + 6) = 63 - y

Use substitution to solve the system by replacing "y" with 4.5x:

4.5 (x + 6) = 63 - 4.5x

4.5x + 27 = 63 - 4.5x

9x + 27 = 63

9x = 36

x = 4

Boat 1: x = 4 mph

Boat 2: x + 6 = 4 + 6 = 10 mph

Answer: 4 mph, 10 mph