In (a)–(d), (i) write a constraint equation, (ii) determine two solutions, and (iii) graph the equation and mark your solutions.
so you ride for 0.72 hours, or \(0.72 \cdot 60 \approx 43\) minutes. So \((2,0.72)\) is one reasonable solution. If you walk for 5 hours, then \(w = 5\), so
so you ride for 0.6 hours, or \(0.6 \cdot 60 = 36\) minutes. So another reasonable solution is \((5, 0.6)\).
so you canoe for about 2.6 hours. So one possible solution is \((3, 2.6)\). If you walk for 1 hour, then \(w = 1\), so
so you canoe for about 3.7 hours. So another possible solution is \((1, 3.7)\).
Commentary
The purpose of this task is to give students practice writing a constraint equation for a given context. Instruction accompanying this task should introduce the notion of a constraint equation as an equation governing the possible values of the variables in question (i.e., "constraining" said values). In particular, it is worth differentiating the role of constraint equations from more functional equations, e.g., formulas to convert from degrees Celsius to degree Fahrenheit. The task has students interpret the context and choose variables to represent the quantities, which are governed by the constraint equation and the fact that they are non-negative (allowing us to restrict the graphs to points in the first quadrant only).
The four parts are independent and can be used as separate tasks.
This task is adapted from Algebra: Form and Function, McCallum et al., Wiley 2010.