math
posted by zshen on .
A boat travels 8km upstream and back in 2 hours. If the current flows at a constant speed of 3km/h, Find the speed of the boat in still water.(when the boat goes upstream, it speed reduces by 3km/h, and when going downstream, its speed increases by 3 km/h)

Let the speed of the boat in still water be x km/h
time upstream = 8/(x3)
time downstream = 8/(x+3)
8/(x3) + 8/(x+3) = 2
times (x+3)(x3)
8(x+3) + 8(x3) = 2(x+3)(x3)
8x + 24 + 8x  24 = 2x^2  18
2x^2 16x  18 = 0
x^2  8x  9 = 0
(x9)(x+1) = 0
x = 9 or x = 1, a negative x is not likely
x = 9
check:
speed upstream = 6 km/h, time = 8/6 or 4/3 hrs
speed downstrem = 12 km/h, time = 8/12 = 2/3 hr
total time = 4/3 + 1/3 = 2
all is good!