AMC 10 · 2020 · #3
Grade 6 rate-ratioPick an answer.
Tool #8 (Analyze the Units) is perfect — the question is built entirely from rates (mile/hour, mile/gallon, /mile, /gallon, /hour). Track units through and the formula writes itself. Tool #7 (Subproblems) splits the work into earnings rate, gas-cost rate, and net rate — all per hour, so we don't even need the total 120 miles. Tool #3 (Eliminate) checks the magnitude: gross is 0.50/mi = $30/hr), so the net must be a bit less than 30 — answers ≤ 20 are out.
Earnings per hour
Distance times the rate gives the hourly earnings.
Speed × pay-per-mile gives pay-per-hour because miles cancel.
Speed multiplied by pay per mile gives pay per hour, because the miles cancel.
▸ Why?
Each rate is a fixed amount of one thing for one unit of another, so the units line up and cancel.
▸ Why?
At a steady speed the distance covered in an hour is exactly that speed, so the chain is legitimate.
Fuel cost per hour
Dividing by the mileage gives the hourly fuel cost.
Chain three rates so miles and gallons both cancel — left with dollars per hour.
6.RP.A.3Identify SubproblemsSubtract for the net
Subtracting shows the two hours never mattered.
Earnings minus the only expense leaves net pay.
4.OA.A.3Identify SubproblemsMatch the choice
The result is 26 dollars an hour.
Net = gross minus expense; only one choice fits the right gap.
6.RP.A.3Eliminate PossibilitiesThis AMC 12 problem only needs Grade 6 "ratios and rates" you already know — earnings 4/hr, net $26/hr.