Question

The cost C of moving rubble is proportional to the product of the mass M of the rubble and the distance D the rubble must be moved. Use K as your proportionality constant (Note: we don't use C since we are already using it for cost).

(a) Find C(M,D).
C(M,D)=___________________
(b) If it costs 50 dollars to move 1 ton of rubble 1 mile, how much does it cost to move 16 tons 15 miles?.
$_____________

Answer 1

a)
`C(M,D) = KMD`

b) $12,000

Explanation:

We are given the following information in the question:

The cost C of moving rubble is proportional to the product of the mass M of the rubble and the distance D the rubble must be moved.

This can be written as:

a)

`C \propto M* D\\C = KMD,\\\text{where K is the constant of proportionality.}`

`C(M,D) = KMD`

b) It costs 50 dollars to move 1 ton of rubble 1 mile

`50 = K* 1* 1\\\Rightarrow K= 50`

We have to find cost to move 16 tons 15 miles.

Putting the values in the function:

`C(16,15) = 50* 16* 15 = 12000`

Thus, $12,00 is the cost to move 16 tons 15 miles.