Question

Emma takes an express train to visit her grandparents each summer. Once the train reaches its cruising speed, it travels at a constant 80 miles per hour for 240 miles before it begins to slow down. The function D(t) represents the distance traveled by the train, in miles, after t hours at cruising speed.
What is the range of D(t)? And is it real or whole numbers?

Answer 1

While cruising the train goes 80t miles in t hours, and it cruises for 240 miles total so t runs from 0 to 240/80 = 3 hours. Thus D(t)=80t for t∈[0,3].

Range: D(t) ∈ [0,240] miles (inclusive). These are real numbers (any real value between 0 and 240), not only whole numbers.