Answer:
3 km/h
Step-by-step explanation:
Let c represent the speed of the current in km/h, and t the time in hours after the raft leaves point A. 2 hours 40 minutes is 8/3 hours.
Distance = Speed × Time
The watercraft meet at a point 27 km upstream from B, so we have two equations involving these variables:
27 = 44 - ct
27 = (12-c)(t -8/3)
Equating these two versions of "27", we have ...
44 -ct = 12t -32 -ct +(8/3)c
76 = 12t + 8/3·c . . . . . add 32+ct
9t +2c = 57 . . . . multiply by 3/4
t = (57 -2c)/9 . . . .solve for t
Now, we can substitute this into the first of the above equations, after rearranging it to ...
ct = 17
c(57 -2c)/9 = 17
2c^2 -57c +153 = 0 . . . . multiply by 9, subtract the left side
c = (57-√((-57)^2 -4(2)(153)))/(2·2) = (57 -√2025)/4 = 12/4 . . . . quadratic formula
c = 3
The speed of the current is 3 km/h.
