Respuesta :
Answer:
6 km/hr or 5 km/hr
Step-by-step explanation:
In the lake, she goes 15 km at x km/hr (named)
In the river, she goes 6 km at x-2 km/hr (current=2 km/hr)
So, the time in the lake - the time in the river = 1 hour (given)
15/x - 6/x-2 = 1 --> x=6;x=5
The speed of the boat as the photographer paddles the lake if the river current is 2 km/h is 6 km/hr and this can be determined by forming the quadratic equation.
Given :
- A wildlife photographer photographs a crocodile and then paddles against a river current for 6 km.
- Then, hoping to photograph a hippopotamus, she paddles 15 km across a lake.
- She paddles across the lake for one hour longer than she paddled up the river.
According to the given data, if the river current velocity is 2 km/hr then let the speed in the lake be x km/hr. So, the speed of the photographer in the river is (x - 2) km/hr
Therefore, the speed of the boat as she paddles the lake if the river current is 2 km/h is given by:
[tex]\dfrac{15}{x} - \dfrac{6}{x-2}=1[/tex]
Now, simplify the above expression.
[tex]15(x-2)-6(x)=x(x-2)[/tex]
[tex]15x-30-6x=x^2-2x[/tex]
[tex]x^2-11x+30=0[/tex]
Factorize the above equation.
[tex]x^2-6x-5x+30=0[/tex]
x(x - 6) - 5(x - 6) = 0
(x - 6)(x - 5) = 0
x = 6 or 5
For more information, refer to the link given below:
https://brainly.com/question/25277954
