Gauge Odom

2022-09-14

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?

Ashlee Ramos

Beginner2022-09-15Added 20 answers

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

$$12({x}^{2}+3x)+5({x}^{2}-3x)=18({x}^{2}-9)$$

$$12{x}^{2}+36x+5{x}^{2}-15x=18{x}^{2}-162$$

$$-{x}^{2}+21x+162=0$$

$${x}^{2}-21x-162=0$$

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

12/x-3 time upstream and 5/x+3 downstream time. We make an equation:

12/x-3+5/x+3=18/x

$$12({x}^{2}+3x)+5({x}^{2}-3x)=18({x}^{2}-9)$$

$$12{x}^{2}+36x+5{x}^{2}-15x=18{x}^{2}-162$$

$$-{x}^{2}+21x+162=0$$

$${x}^{2}-21x-162=0$$

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

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