Q43. - Algebra 1

Question

The table shows the distance travelled by sound in water. Write an equation for this sequence. Then find the time for sound to travel 72,300 feet.

Time (s)	1	2	3	4
Distance (ft)	4820	9640	14460	19280

Step-by-Step Solution

Answer

The equation for this sequence is $y=4820x$.

The time taken by sound to travel 72,300 feet is 15 seconds.

Step 1. Observe the table and find the equation for the sequence.

Calculate the difference between the times and distances.

From the above table it can be noticed that the difference between the times is 1 and the difference between the distances is 4820.

 

This implies the value of constant of variation (k) is given by:

$$\begin{gathered} k=\frac{4820}{1} \\ =4820 \end{gathered}$$ 

As, the value of k is 4820. Therefore, the equation for this sequence is given by:

$$\begin{gathered} y=kx \\ y=4820x \end{gathered}$$ 

Where x and y represents the time and distance respectively.

Step 2. Find the time taken by sound to travel 72,300 feet.

The distance is 72,300 feet. Therefore, the value of y is 72300.

 

The time taken by sound to travel 72,300 feet is given by:

$$\begin{gathered} y=4820x \\ 72,300=4820x \\ \frac{72300}{4820}=x \\ 15=x \end{gathered}$$ 

Therefore, the time taken by sound to travel 72,300 feet is 15 seconds.