17.3k views
0 votes
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.

User Axil
by
6.1k points

1 Answer

4 votes

Answer: S=18

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