Speed vs Time Relationships

Algebra 2 · Axiom Academy

On a fixed 120-mile trip the travel time is — your first rational function. Push the speed up and the clock shrinks; ease it down and the clock stretches. One trip, 120 miles — how long does it take? Every drive trades two numbers against each other: how fast you go, and how long you're on the road. Pin the distance at 120 miles and those two numbers lock into a single rule — one you can watch unfold before you drive it yourself. Because the distance is fixed at 120 miles, the time is simply : 120 divided by your speed. Watch the point trace that rule — as the speed climbs along the bottom, the time is read straight off the curve, and it falls. Speed and time move in opposite directions — that is an inverse relationship. Drag the speed slider — or grab the point on the curve. At every speed the time is . Speed up and the time falls; slow down and it climbs. They always pull opposite ways. Double the speed and you halve the time: 60 mph takes 2 hours, 120 mph just 1. What happens as the speed nears zero? Now creep the speed down toward a crawl. The slower you go, the more the time balloons — 5 mph already means a full day on the road, and 1 mph drags out to 120 hours, five whole days. The time never stops growing, and the curve never touches the line v = 0 . That runaway climb is a vertical asymptote — the fingerprint of a rational function. You just met a rational function

This is the written version of the interactive lesson above. See the full Algebra 2 course.