AMC 10 · 2003 · #4
Grade 6 rate-ratioPick an answer.
The word "speed" with a target unit of km/hr is a signal for Tool #8 (Analyze the Units): average speed is defined as (total distance in km)/(total time in hr), so the units themselves tell us exactly what to collect — a total distance and a total time — and warn us to convert minutes to hours before dividing. Tool #7 (Identify Subproblems) then splits the job cleanly: first add up the distance, separately add up the time, and only at the end combine them. The units framing also guards against the classic trap of averaging the two speeds (2 and 6) to get 4, which mixes rates instead of dividing one total by another.
Read the target unit
The unit tells the recipe: average speed is total distance over total time.
The unit "km per hr" literally reads as kilometres divided by hours, so it names the two totals you must gather.
6.RP.A.3Analyze The UnitsAdd distance and time
The trip covers 2 km in 40 minutes, which is 2/3 of an hour.
Keep the two piles separate — distance is just 1+1, and time only becomes usable once it is in hours to match the km/hr goal.
5.MD.A.1Identify SubproblemsDivide totals for the speed
Dividing gives 2 divided by 2/3 = 3 km per hour, choice (A).
Splitting 2 km over 2/3 of an hour is the same as asking how far she goes in a full hour, and 2 ÷ 2/3 scales it up to 3.
Splitting the total distance over the total time gives the speed the question asks for.
▸ Why?
At a steady pace the distance is the speed times the time, so any two of the three fix the third.
▸ Why?
An hour is always the same fixed count of minutes, so the times can be renamed into one unit before dividing.
Average speed is all your distance divided by all your time — never just the average of the two speeds, because the slow part eats up more of the clock.
- Read the target unit
- Add distance and time
- Divide totals for the speed