MATH SOLVE

3 months ago

Q:
# 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.

Accepted Solution

A:

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