Competition · AMC preparation · step 4 of 4
AMC 8 · 2008 · #5
Grade 6 rate-ratioPick an answer.
AMC 8 2008 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.
Average speed is defined by a single equation: speed = distance ÷ time, so Tool #3 (Write an Equation) is the direct route. The two pieces of that equation — total distance and total time — are not handed to us, so Tool #7 (Identify Subproblems) helps us break the work into two small steps: first find the distance from the odometer change, then add the two riding times.
Find the total distance
The odometer is a running total, so subtract the readings: the trip covers 220 miles.
Subtracting multi-digit whole numbers is a Grade 4 skill. The odometer is a running total, so the difference is exactly the new miles.
4.NBT.B.4Identify SubproblemsFind the total time
Barney rode 4 hours then 6 hours, so the total riding time is 10 hours.
Combining the two riding sessions into one total is a Grade 4 multi-step word problem move.
4.OA.A.3Identify SubproblemsDivide distance by time
Divide total distance by total time: 220 ÷ 10 gives an average speed of 22 mph → (E).
Miles per hour is a unit rate: how many miles for each 1 hour. Dividing 220 by 10 gives that per-hour amount.
The average speed over the whole ride is the total distance divided by the total time.
▸ Why?
Average speed is the one steady miles-per-hour that would cover the whole distance in the whole time, so finding it means splitting the total distance evenly across every hour ridden.
▸ Why?
At a steady speed each hour adds the same number of miles, so the total distance is that per-hour amount stacked up once for every hour — the per-hour miles times the number of hours.
▸ Why?
Because total distance equals the per-hour miles times the hours, pulling the per-hour miles back out means undoing that multiplication, and division is exactly what undoes multiplication.
Average speed is just total distance divided by total time. Get each piece in its own step, then do one division.
- Find the total distance
- Find the total time
- Divide distance by time
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