Question

An alligator's tail length,t, varies directly as its body length,b. an alligator with a body length of 4 feet has a tail length of 2.5 feet. what is the tail length of an alligator whose body length is 3.2 feet?

Answer 1

Here we are given that the Alligator's tail length t varies directly as its body length b.

Using this given information and taking k as constant of proportionality, we get this equation :

$t=kb$.................(1)

Now we are given:

body length (b) = 4 feet

tail length (t) = 2.5 feet

plugging these values in equation (1) we have,

$2.5=k*4$

from here we can calculate the value of k, dividing both sides by 4

k=2.5/4 = 0.625.............(2)

Now we have to find tail length of alligator if body length is 3.2 feet.

so plugging b=3.2 and k=0.625 in equation (1)

$t=3.2 * 0.625$

t= 2

So tail length is 2 feet when body length of alligator is 3.2 feet.