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

4 mph, 10 mph

geometry: triangles

solvers

lessons

answers archive

call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584

where is the graph? need more info