Question

BITANA MOUNTAIN 3.3: Pittsburgh to Phoenix On its way from New York to San Diego, a plane flew over Pittsburgh, Saint Louis, Albuquerque, and Phoenix traveling at a constant speed. Ivan Vos . CES *** A MEXICO Tem Complete the table as you answer the questions. Be prepared to explain your reasoning Crates

Answer 1

Speed is defined as the distance travelled per unit time,

`\text{ Speed}=\frac{\text{ Total distance travelled}}{\text{ Total time taken}}`

First of all, consider the first row,

`\begin{gathered} \text{Distance}=550\text{ miles} \\ \text{ Time}=1\text{ hour} \end{gathered}`

Then the speed of the plane is calculated as,

`\begin{gathered} \text{ Speed}=\frac{550\text{ miles}}{1\text{ hour}} \\ \text{ Speed}=550\text{ miles per hour} \end{gathered}`

So the speed of the plane is 550 miles per hour.

So, in the first row, the speed cell should be filled with 550 miles per hour.

Given that the plane has constant speed throughout the journey, so the value 550 miles per hour should also be filled in the speed column in the remaining two rows.

Now, consider the second row,

`\text{ Time}=1\text{ hour 42 minutes}`

Convert the time into hours,

`\begin{gathered} \text{ Time}=1\text{ hour 42 minutes} \\ \text{ Time}=1\text{ hour }+\text{ 42 minutes} \\ \text{ Time}=1\text{ hour }+\text{ 42}\cdot\text{(1 minute)} \\ \text{ Time}=1\text{ hour }+\text{ 42}\cdot\text{(}(1)/(60)\text{ hour)} \\ \text{ Time}=1\text{ hour }+0.7\text{ hour} \\ \text{ Time}=1.7\text{ hour} \end{gathered}`

Substitute the values of speed and time corresponding to the second row,

`\begin{gathered} 550=\frac{\text{ Distance from Saint Louis to Albuquerque}}{\text{1}.7} \\ \text{Distance}=550\cdot(1.7) \\ \text{Distance}=935 \end{gathered}`

So the distance between Saint Louis to Albuquerque is 935 miles. So the distance column in the 2nd row will contain the value 935 miles.

Now, consider the third row,

`\begin{gathered} \text{Distance }=330\text{ miles} \\ \text{ Speed}=550\text{ miles} \end{gathered}`

So the missing value of 'time' can be calculated as,

`\begin{gathered} 550=\frac{330}{\text{Time}} \\ \text{Time}=(330)/(550) \\ \text{Time}=0.6 \end{gathered}`

So the third row will have the entry ' 0.6 hours' under the first column.

The complete table will be obtained as follows,

1.

The distance between Saint Louis to Albuquerque can be observed from the table as 935 miles.

2.

The time taken to travel from Albuquerque to Phoenix can be observed from the table as 0.6 hour.

3.

From the table, it can be observed that the distance values vary in accordance with the time values. To cover more distance, the plane will need more time. And for lower distance, the plane will need lesser time. It follows that that time is directly proportional with distance,

`\text{Distance}\propto\text{ Time}`

Thus, the table represents the proportionality relationship between distance travelled and the time taken to travel that distance.

4.

Consider that the constant of proportionality be speed.

`\begin{gathered} \text{ Distance}=\text{Speed}\cdot\text{ Time} \\ \text{Speed}=\frac{\text{ Distance}}{\text{ Time}} \end{gathered}`

The value of this constant 'speed' can be calculated by taking sample values.

From the first row, we have

`\begin{gathered} \text{Distance}=550\text{ miles} \\ \text{ Time}=1\text{ hour} \end{gathered}`

The corresponding value of speed is calculated above as 550 miles per hour.

So the constant can be considered as 550 in the units, miles per hour. This means the claim made by Diego is right.

Now, consider the time in minutes, the given information becomes,

`\begin{gathered} \text{Distance}=550\text{ miles} \\ \text{ Time}=1\text{ hour}=60\text{ minutes} \end{gathered}`

Then the corresponding speed will be,

`\begin{gathered} \text{Speed}=(550)/(60) \\ \text{Speed}=(55)/(6) \\ \text{Speed}=9(1)/(6)\text{ miles per minute} \end{gathered}`

Thus, the claim made by Andre is also correct.

Therefore, it can be concluded that both claims are true, the difference lies in the units of the constant used.