Question

A certain tiger shark is 55 cm long at birth and grows 2.5 cm / year. A certain hammerhead shark is 25 cm long at birth and grows 5 cm/year. When will the sharks be equal in length? Let x = time in yearsLet y = length of the sea creaturesThe equation for the length of the tiger shark is ___. The equation for the length of the spiny dogfish hammerhead shark is ___. Solving with elimination, the sharks will be equal in length when ___ years have passed.

Answer 1

Let x = time in years;

Let y = length of the sea creatures;

For both sharks, we can describe their growth with a linear equation since they grown in a constant rate. A line equation written in slope-intercept form is

`y=mx+b`

Where m represents the slope(or the rate of growth) and b represents the y-intercept(in our problem, the initial length).

A certain tiger shark is 55 cm long at birth and grows 2.5 cm/year, therefore, its growth can be represented by the following equation:

`y_t=2.5x+55`

A certain hammerhead shark is 25 cm long at birth and grows 5 cm/year, therefore, its growth can be represented by the following equation:

`y_h=5x+25`

The length of the sharks will be equal when the value of those functions are the same. The solution for the following equation is the corresponding time in years

`\begin{gathered} y_t=y_h \\ 2.5x+55=5x+25 \\ 5x-2.5x=55-25 \\ 2.5x=30 \\ x=(30)/(2.5) \\ x=12 \end{gathered}`

Their length will be the same after 12 years.