AMC 10 · 2015 · #2
Grade 4 rate-ratioPick an answer.
AMC 10 2015 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.
The hidden trap is the word "second": finishing the second task means two equal tasks are complete, not one. Tool #7 (Identify Subproblems) splits the work into three clean pieces — count how many tasks the elapsed time covers, find the minutes per task, then add one more task. Tool #8 (Analyze the Units) keeps the rate honest: "100 minutes for 2 tasks" becomes "50 minutes per task," and minutes per task is the unit that lets us extend to the third task. Tool #3 (Eliminate Possibilities) explains the wrong choices, which come from dividing the elapsed time by 3 instead of 2.
Count the finished tasks
By 2 : 40 PM both the first and second tasks are done — that is two equal tasks, not one.
"Finishes the second task" means both task 1 and task 2 are over, so the clock has covered two whole tasks.
4.OA.A.3Identify SubproblemsMeasure the elapsed time
From 1 : 00 PM to 2 : 40 PM is 1 hour 40 minutes, which is 100 minutes for the two tasks.
Adding the 60 minutes of the full hour to the extra 40 minutes turns the clock gap into one plain number of minutes.
3.MD.A.1Analyze The UnitsFind minutes per task
Split the 100 minutes evenly between the two tasks: that is 50 minutes per task.
Dividing total minutes by the number of tasks cancels "tasks" and leaves the time for a single task.
4.OA.A.3Analyze The UnitsAdd the third task
The third task also takes 50 minutes, so 2 : 40 PM plus 50 minutes lands on 3 : 30 PM.
Carrying the minutes past the next hour mark adds one more 50-minute task onto the clock, landing on 3 : 30 PM.
3.MD.A.1Analyze The UnitsFinishing the "second" task means two tasks are done, so split the time between two, not three.
- Count the finished tasks
- Measure the elapsed time
- Find minutes per task
- Add the third task