Answer:
12 km
Step-by-step explanation:
Let
x km/h = speed of the canoe on the lake
y km/h = speed of the current
With the current:
Speed = x + y km/h
Distance = 30 km
Time = 3 hours 20 minutes = [tex]3\dfrac{1}{3}[/tex] hours
Thus,
[tex]30=3\dfrac{1}{3}(x+y)\\ \\30=\dfrac{10}{3}(x+y)\\ \\90=10(x+y)\\ \\x+y=9[/tex]
Against the current:
Speed = x - y km/h
Distance = 28 km
Time = 4 hours
Thus,
[tex]28=4(x-y)\\ \\x-y=7[/tex]
Add these two equations:
[tex]x+y+x-y=9+7\\ \\2x=16\\ \\x=8\ km/h[/tex]
On the lake:
Time = 1.5 hours
Speed = 8 km/h
Distance [tex]=8\cdot 1.5=12\ km[/tex]
