A tourist ignores the warning signs and leaves food in his car while he goes for a hike. A mama bear and her cub open the car door in six seconds. How long would it take each bear to open the car door alone if the cub needs 9 more seconds than the mama bear?

Respuesta :

Answer:

0 sec. I help him get the tourist too :)

Step-by-step explanation:

jk, but her cub takes 13 and the mama 4

Using the together rate, it is found that it would take each bear 9 hours to open the car door alone.

What is the together rate?

The together rate is the sum of each separate rate.

In this problem, the rates are as follows:

  • Together rate: 1/6.
  • Mama's rate: 1/x.
  • Cub's rate: 1/(x + 9).

Hence:

[tex]\frac{1}{x} + \frac{1}{x + 9} = \frac{1}{6}[/tex]

[tex]\frac{x + 9 + x}{x(x + 9)} = \frac{1}{6}[/tex]

[tex]x^2 + 9x - 12x - 54 = 0[/tex]

[tex]x^2 - 3x - 54 = 0[/tex]

Quadratic equation with coefficients [tex]a = 1, b = -3, c = -54[/tex], hence:

[tex]\Delta = b^2 - 4ac = (-3)^2 - 4(1)(-54) = 225[/tex]

[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a} = \frac{3 + \sqrt{225}}{2} = 9[/tex]

[tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a} = \frac{3 - \sqrt{225}}{2} = -6[/tex]

It would take each bear 9 hours to open the car door alone.

To learn more about the together rate, you can take a look at https://brainly.com/question/25159431