Problem

A trip covers \(d(t)=120~\text{miles}\) in \(t~\text{hours}\). Form the average-speed function \(r(t)=d(t)/t\), state its units, give both the algebraic restriction and the contextual real-time domain, and interpret the quotient.

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quotient expression=r(t)=120/t; simplified=120/t; output units=miles/hour; algebraic restriction=t≠0; contextual domain=t∈(-∞,0)∪(0,∞); interpretation=allows negative travel time

quotient expression=r(t)=120/t; simplified=120/t; output units=miles/hour; algebraic restriction=t≠0; contextual domain=t>0 real hours; interpretation=distance divided by positive travel time

quotient expression=r(t)=120/t; simplified=120/t; output units=miles total; algebraic restriction=t≠0; contextual domain=t>0; interpretation=incorrectly retains distance units

quotient expression=r(t)=120t; simplified=120t; output units=miles/hour; algebraic restriction=none; contextual domain=t>0; interpretation=multiplies distance by time instead of dividing

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A trip covers \(d(t)=120~\text{miles}\) in \(t~\text{hours}\). Form the average-speed function \(r(t)=d(t)/t\), state its units, give both the algebraic restriction and the contextual real-time domain, and interpret the quotient.

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