Question

Two dogs, Rufus and Daisy, are eating dinner. The amount of food (measured in grams) and Rufus's bowl after t minutes is R(t) = 450-150t, and the amount of food (measured in grams) in Daisy's bowl after t minutes is D(t)= 400 - 120t. Express the ratio of the amount remaining in Daisy's bowl to the amount remaining in Rufus's bowl as a rational function, and simplify.

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Answer 1

A.

Explanation:

So we want the ratio of the food amount in Daisy's bowl (D) to the food amount in Rufus's bowl (R) at time t.

So we are asked to do:

`(D)/(R)`

`(400-120t)/(450-150t)`

Let's see if we can simplify any.

Every single term on top and bottom have a common factor of 10 since they each contain a factor that ends in 0.

I'm going to divide top and bottom by 10:

`(40-12t)/(45-15t)`

The answer is A.

I can see no more common factors between 40,12t,45, and 15t:

40=2(2)(2)(5)

12t=2(2)(3)t

45=3(3)(5)

15t=3(5)t

They don't all contain a common factor when looked at altogether.