Question 82170
Let x=time, y=distance

Since we have a relationship between the time and distances, we can say that these times and distances follow a pattern. We can find the formula for this pattern by letting x=1 second and y=1100 to get one point (1,1100). Now let x=2 and y=2200. Now that we have 2 points (1,1100) and (2,2200) and we can now make a line


*[invoke calculating_slope 1, 1100, 2, 2200]


So we can see that equation is {{{y=1100x}}}. We can check this by plugging in x=1 to get


{{{y=1100(1)}}} Plug in x=1


{{{y=1100}}} works

And we can do this for every x to verify.




For the second problem, we're going to make equations of the two plans and find out where they intersect:

So $20 an hour translates to this equation:

{{{y=20x}}}


and $8 per hour + $12 translates to:


{{{y=8x+12}}}


So now set them equal to each other to see when the plans will be the same


{{{20x=8x+12}}}


{{{20x-8x=cross(8x-8x)+12}}} Subtract 8x from both sides


{{{12x=12}}}


{{{cross(12/12)x=12/12}}} Divide both sides by 12


{{{x=1}}} 


So the plans are equal at x=1, which is 1 hour.