Answer: S=18
Step-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 / factor
9S - 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
