Question

1. Write a linear equation of the form y1 = mx + b for your first set of data.2. Write a linear equation of the form y2 = mx + b for the other equation in your system. 3. How many round trips in a 12-hour day can each mode of transportation produce?

Answer 1

Given the distance of 382 miles, and a velocity of 760 miles/hour and a time of 0.583 hour, we can writte the following equation:

`382\text{ miles}=760(miles)/(hour)*0.583hour+b`

Then the intercept b is:

`\begin{gathered} b=382-760*0.583 \\ b=-61.08\text{ miles} \end{gathered}`

Hence the equation for the first data set is:

`distance=0.583*speed-61.08`

Now the next dataset:

`\begin{gathered} 382miles=(535miles)/(hour)*1.25hour+b \\ b=-286.5\text{ miles} \end{gathered}`

Hence the equation for the second point is:

`distance=1.25*speed-286.5`

Next, for the third point. By hyperloop, a round trip takes 0.583*2=1.166 hour (go and back), hence in a 12-hour day:

`(12)/(1.166)=10.29\text{ trips}`

Hence by hyperloop we got 10 trips.

On the other way, by airplane it takes 1.25*2=2.5hour:

`(12)/(2.5)=4.8\text{ trips}`

Then by airplane we got 4 round trips.