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 \\ (16)/(24)=(24k)/(24) \\ k=(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(2)/(3) \\ d=(2)/(3) \end{gathered}`

Distance = 10 feet

`\begin{gathered} 10=t\cdot(2)/(3) \\ 10\cdot(3)/(2)=t\cdot(2)/(3)\cdot(3)/(2) \\ (30)/(2)=t\cdot1 \\ t=15 \end{gathered}`

Time = 45 sec

`\begin{gathered} d=45\cdot(2)/(3) \\ d=(90)/(3) \\ d=30 \end{gathered}`

Answer:

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

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