Travelling along Geometry

$1.$ Let our trip be a line that passes through the given points $(1,110)$ and $(1.5,85)$ , taking time on the $x-coordinate$ and distance on the $y-coordinate$ (as time is independent over distance). If we find the slope of the given points, it will serve as the speed $s$ at which we are travelling, i.e. $s=\frac { y_2-y_1 }{ x_2-x_1 } =\frac { 85-110 }{ 1.5-1 }$ $\Longrightarrow \boxed{s=|50|mph}$ $2.$ Using the same logic, to find the total distance, $y-intercept$ of the above given point will serve as the total distance of our trip. Using slope-point form: $y-y_1=m(x-x_1)\ ; at\ (1,110)$ $\Longrightarrow y-110=-50(x-1)$ $\Longrightarrow y=-50x+160$ By comparing it with the equation $y=mx+d$ , (where $d$ is the $y-intercept$ ) we can easily deduce our total distance; i.e. $\boxed{d=160miles}$ $3.$ Again the same logic, to find the total time, $x-intercept$ of the above given point will serve as the total time of our trip (from the start until we arrive). Using two intercept form: $\frac { x }{ t }+\frac { y }{ d }=1\ ; at\ (1,110)$ where $t$ & $d$ are $x\ and\ y-intercepts$ respectively. $\Longrightarrow \frac { 1 }{ t }+\frac { 110 }{ 160 }=1$ $\Longrightarrow \boxed{t=3.2hours}$