Speed Comparison

Pre-Algebra · Axiom Academy

A speed is just a unit rate — distance per one unit of time. Once two speeds share that same basis, the bigger number really is faster. Suppose a walker covers 6 miles in 2 hours at a steady pace. That's a rate — miles compared to hours — but it's awkward to compare because it's spread over 2 hours. A unit rate rewrites it as the distance for one hour: divide the distance by the time. The animation marks off each hour and reads the distance per single hour. A rate becomes a speed when you divide to a per-one-unit basis 6 miles in 2 hours is 3 miles every 1 hour 2. To Compare, Use the Same Basis Now race two walkers. The red walker goes 12 miles in 4 hours; the blue walker goes 15 miles in 3 hours. You can't tell who's faster from "12" vs. "15" — the times differ. Reduce each to its unit rate (miles per one hour) and they line up on the same basis. The animation runs both for 1 hour and reads off how far each gets in that single hour. On the same per-hour basis, 5 beats 3: The blue walker is faster — even though 12 looked like a big number for the red walker. 3. Same Units: 30 mph vs. 45 ft/s Back to the opening race. Both speeds are already unit rates (each is "per one " of something), but the units don't match: one is miles per hour , the other feet per second . To compare, convert one speed so both use the same units. We'll turn 30 mph into feet per second using two facts: there are 5,280 feet in a mile and 3,600 seconds in an hour . Now both speeds are in feet per second:

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