Question

Team ATime Distance(hours) (miles)Team BTime Distance(hours)(miles)12.52363 10.04 20.05 40.0leTeooم ع سیa.For which team is distance proportional to time? Explain your reasoning.

Answer 1

As per given by the question,

There are given that the two teams, A and B.

Now,

For team A,

$\begin{gathered} \text{Time }\rightarrow Dis\tan ce \\ 1\rightarrow2.5 \\ 2\rightarrow5 \\ 3\rightarrow7.50 \\ 4\rightarrow10 \\ 5\rightarrow12.5 \\ 6\rightarrow15 \end{gathered}$

And,

For team B;

$\begin{gathered} \text{Time}\rightarrow\text{ Distance} \\ 1\rightarrow4 \\ 2\rightarrow6 \\ 3\rightarrow8 \\ 4\rightarrow10 \\ 5\rightarrow12 \\ 6\rightarrow14 \end{gathered}$

Now,

(a):

According to the table,

Distance is proportional to time for team A.

Since, all the ratio comparing to the time are equavalent , the value of each ratio is 2.5.

Hence, team A is distance proportional to the time.

(b):

For team B, the ratio are not equavalent.

Because ;

The value of the ratio are

$4,\text{ 3, 2}\frac{2}{3},\text{ 2.5, 2.4, 2}\frac{1}{3}$