Identify as a direct variation, inverse variation or neither. the number of tons of coal burned by an old coal burning locomotive under given conditions varies as the number of hours.

it is a direct variation.

Justification:

In a direct variation the variables are related by a proportionality constant in this way:

y = k x

Tthan means that the value of y is always the product of a constant times the value of x.

The situation discribed for the coal may be written as:
number of tons of coal burned: c

number of hours: h

⇒ c = k × h

Which is that you can calcualte the number of tons of coal burned at any time, once you know the proportionality constant k.