# math

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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)

• math -

Let the speed of the boat in still water be x km/h

time upstream = 8/(x-3)
time downstream = 8/(x+3)

8/(x-3) + 8/(x+3) = 2
times (x+3)(x-3)

8(x+3) + 8(x-3) = 2(x+3)(x-3)
8x + 24 + 8x - 24 = 2x^2 - 18
2x^2 -16x - 18 = 0
x^2 - 8x - 9 = 0
(x-9)(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!

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