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Question

 A boat traveled 5 km with the stream and 6 km against the stream spending in total of 1 hour. Find the speed of the boat while travelling with the stream if the current of the stream is 3 km/hour.

Answer 1

distance = speed x time

let r= speed of the boat in still water = 12 km/hr

speed of the boat going with the water = 3 + 12 = 15 km/hr

speed of the boat going against the water = 12-3 = 9 km/hr

let t = time traveled with the stream = 1/3 hour = 20 minutes

time traveled against the stream = 2/3 hour = 40 minutes

6=(r-3)t = (12-3)(2/3) = 9 x 2/3 = 6 km

5=(r+3)(1-t) = (12+3)(1-2/3) = 15 x 1/3 = 5 km

Answer 2

distance=rate*time

d=r*t

let r=speed of the boat

5=(r+3)t

6=(r-3)(1-t)

from the first equation you get t=5/(r+3)

substitute into the second equation

6=(r-3)(1-[5/(r+3])

6=(r-3)([r+3-5]/[r+3])

6=(r-3)([r-2]/[r+3])

multiply both sides by (r+3)

6(r+3)=(r-3)(r-2)

6r+18=r^2-5r+6

r^2-5r+6-6r-18=0

r^2-11r-12=0

factor

(r-12)(r+1)=0

disregard r+1=0 because r=-1

r-12=0

r=12 km per hour is the rate of the boat