15 POINTS: A motorboat traveling downstream covers the distance between port M and port N in 6 hours. Once, the motorboat stopped 40 km before reaching N, turned around, and returned to M. This took the motorboat 9 hours. Find the speed of the motorboat in still water if the speed of the current is 2 km/hour.

Answer: S=18Step-by-step explanation:D = distance between M and N  S = speed of the boat  S + 2 = speed down streem  S - 2 = speed upstream  T = time on the downstream leg until the boat made its turn  9-T= time on the upstream leg   6(S + 2) = D  T (S + 2) = D - 40  (9-T)(S-2) = D - 40  now we have 3 equations and 3 uknowns  lets multply everything out  6S + 12 = D  ST + 2T = D - 40  9S - 18 - ST + 2T = D - 40  add the second 2 together to get rid of the ST term  9S - 18 + 4T = 2D - 80  and lest subtract them from one annother   2ST - 9S + 18 = 0  if we can find T in terms of S we will have a quadratic equation, and will be able to use the quadratic formula / factor9S - 18 + 4T = 2(6S + 12) - 80  9S - 18 + 4T = 12 S + 24 - 80  4T = 3S - 38   T = 0.75 S - 9.5  2S(0.75 S - 9.5) - 9S + 18 = 0   1.5 S^2 - 28 S + 18 = 0   S = 18, 2/3  now it doesn't make sense for S to equal -2/3 as it suggests the boat moves backward when it is going up stream. (and that it travels downstream for negative time)   S = 18