1. Hyperloop Data:
y = 760*x - 61.08
2. Plane Data:
y = 535*x - 286.75
So we are given a few pieces of information in the question. We are told by the data that it takes the hyperloop 35 minutes to travel from LA to SF and it takes the plane 1 hr 15 min to travel from LA to SF. We are also given the speed of both transportation methods. We can use the speeds as the slope of both equations, and we can find the y-intercept by using the time as the x-value.
First we need to convert both units of time to hours, so that the data is consistent.
35 minutes can be converted to 0.583 hours, and 1 hr 15 minutes can be converted to 1.25 hours. Now, since we know that it takes 0.583 hours and 1.25 hours to travel a distance of 382 miles, we can use the points (0.583, 382) and (1.25, 382) for our calculations, and again, we will use the speeds as the slope. We now have the following equations:
382 = 760*(0.583) + b
382 = 535*(1.25) + b
We can solve both equations for b, such that we have the following:
382 = 760*(0.583) + b
382 = 443.08 + b
b = -61.08
382 = 535*(1.25) + b
382 = 668.75 + b
b = -286.75
In this case, the negative y intercepts represent the distances (or obstacles) that each mode of transportation needs to overcome to complete the trip. Since the hyperloop has a higher y-intercept (lower negative number), it has less distance to overcome and is more effecient (timewise) than air travel by plane.