(f) Then [D/(16 - R)] (12 - R) = D - xand [D/(21 - R)] (12 - R) = x(g) [D/(16 - R)] (12 - R) = D - x ---> (12 - R)/(16 - R) = 1 - x/D and(h) [D/(21 - R)] (12 - R) = x --->(12 - R)/(21 - R) = x/D(i) (12 - R)/(16 - R) = 1 - x/D = 1 - (12 - R)/(21 - R)(j) (12 - R)(21 - R) = (16 - R)[21 - R - (12 - R)] = (16 - R)8 --->(k) 252 - 33R + R^2 = 128 - 8R ---> R^2 - 25R + 124 = 0 ---> (l) R = [25 ± sqrt(25^2 - 4(124))]/2 = [25 ± 11.3578]/2 ---> R = 6.8211 (only valid solution)Thus, R = 6.8211 hours = 6:49 AM-sally speed xbob speed ydistance zsunrise w amz=4x+9y4x +9y / 21-w = y4x +9y / 16-w = x4x/y -12 = 9 y/x - 12x = 1.5 ytotal distance = 15 y out of 9y was after noon so 6y was before therefore sunrise at 6-6:42 for me.......
(d) They pass each other at noon (12 hours) = 12 - R.
(e) Let D - x = the distance Sally has traveled when they cross, then x = the distance
Bob has traveled at that time.
(f) Then [D/(16 - R)] (12 - R) = D - x and [D/(21 - R)] (12 - R) = x
(g) [D/(16 - R)] (12 - R) = D - x ---> (12 - R)/(16 - R) = 1 - x/D and
(h) [D/(21 - R)] (12 - R) = x --->(12 - R)/(21 - R) = x/D
(i) (12 - R)/(16 - R) = 1 - x/D = 1 - (12 - R)/(21 - R)
(j) (12 - R)(21 - R) = (16 - R)[21 - R - (12 - R)] = (16 - R)8 --->
(k) 252 - 33R + R^2 = 128 - 8R ---> R^2 - 25R + 124 = 0 --->
(l) R = [25 ± sqrt(25^2 - 4(124))]/2 = [25 ± 11.3578]/2 ---> R = 6.8211 (only valid solution)
Thus, R = 6.8211 hours = 6:49 AM
6:42 for me.
