# The boat traveled 12 km upstream and 5 km downstream. At the same time, he spent as much time as he would need if he walked 18 km across the lake. What is the speed of the boat if it is known that the speed of the river is 3 km/h?

The boat traveled 12 km upstream and 5 km downstream. At the same time, he spent as much time as he would need if he walked 18 km across the lake. What is the speed of the boat if it is known that the speed of the river is 3 km/h?
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Ashlee Ramos
Let's denote the speed of the boat as x, then the speed upstream is x-3, and downstream is x+3.
12/x-3 time upstream and 5/x+3 downstream time. We make an equation:
12/x-3+5/x+3=18/x
$12\left({x}^{2}+3x\right)+5\left({x}^{2}-3x\right)=18\left({x}^{2}-9\right)$
$12{x}^{2}+36x+5{x}^{2}-15x=18{x}^{2}-162$
$-{x}^{2}+21x+162=0$
${x}^{2}-21x-162=0$
D=441+648
D=1089
x1=(21-V1089)/2=-6-foreign root, because speed cannot be "-"
x2=(21+V1089)=54/2=27
27 km/h - boat's own speed