Question

Jessica reads a story about a turtle that swam 16 feet in 24 seconds. She assumes that the time t that it takes the turtle to swim a distance of d feet is a proportional relationship.Jessica starts to create the table shown for other times and distances the turtle swims.

Answer 1

Equation to represent this proportional relationship is d = tk, where t is time, d is distance and k is the constant of proportionality.

Therefore, given d = 16 and t = 24, we substitue in the above equation and find k:

$\begin{gathered} d=tk \\ 16=24k \\ \frac{16}{24}=\frac{24k}{24} \\ k=\frac{2}{3} \end{gathered}$

Next let's complete the table by substituting the value of k and the other given value of t or d, as the case may be:

Time = 1 sec

$\begin{gathered} d=tk \\ d=1\cdot\frac{2}{3} \\ d=\frac{2}{3} \end{gathered}$

Distance = 10 feet

$\begin{gathered} 10=t\cdot\frac{2}{3} \\ 10\cdot\frac{3}{2}=t\cdot\frac{2}{3}\cdot\frac{3}{2} \\ \frac{30}{2}=t\cdot1 \\ t=15 \end{gathered}$

Time = 45 sec

$\begin{gathered} d=45\cdot\frac{2}{3} \\ d=\frac{90}{3} \\ d=30 \end{gathered}$

Answer:

Time (seconds): 1 | 15 | 24 | 45

Distance (feet): 2/3 | 10 | 16 | 30