Depth · one concept from first principles · step 2 of 4
A covers 24 m in 3 s, so y/x is the same everywhere on A's line.
On a line through the origin, y/x is the constant of proportionality: 8 meters each second.
7.RP.A.2Convert To AlgebraA runs a steady m every second, so A's line is .
A straight line from O means A gains the same distance every second, so distance is speed times time.
m in seconds means m each second, because division undoes .
Doubling or tripling the time does the same to the distance, so stays all along the line.
B covers the same 24 m but needs 4 s.
B is slower: 6 meters each second.
7.RP.A.2Convert To AlgebraPut y = 100 into each equation and solve for x.
Time = distance ÷ speed: 100 ÷ 8 and 100 ÷ 6 seconds.
7.RP.A.2Analyze The UnitsB finishes later, so subtract A's time from B's using a common denominator.
Rewrite both times in sixths, then subtract.
7.NS.A.1Identify SubproblemsOne point on a line through the origin tells you the whole line: divide y by x.
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