AMC 10 · 2015 · #2
Easy mode Grade 4Marie does three jobs one after another, with no breaks. Each job takes the same amount of time. She starts the first job at 1:00 PM. She finishes the second job at 2:40 PM. What time does she finish the third job?
Pick an answer.
AMC 10 2015 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.
Try it yourself first — the explanation is most useful after you’ve attempted it.
Toolkit + CCSS Solution
Understand
Restated: Marie does three tasks back to back, with no breaks, and each task takes the same amount of time. She starts the first task at $1\!:\!00$ PM and finishes the second task at $2\!:\!40$ PM. Find the clock time when she finishes the third task.
Givens: Three tasks done in a row with no breaks; All three tasks take equal time; First task starts at $1\!:\!00$ PM; Second task finishes at $2\!:\!40$ PM; Answer choices: (A) 3:10 PM, (B) 3:30 PM, (C) 4:00 PM, (D) 4:10 PM, (E) 4:30 PM
Unknowns: The clock time when the third task finishes
Understand
Restated: Marie does three tasks back to back, with no breaks, and each task takes the same amount of time. She starts the first task at $1\!:\!00$ PM and finishes the second task at $2\!:\!40$ PM. Find the clock time when she finishes the third task.
Givens: Three tasks done in a row with no breaks; All three tasks take equal time; First task starts at $1\!:\!00$ PM; Second task finishes at $2\!:\!40$ PM; Answer choices: (A) 3:10 PM, (B) 3:30 PM, (C) 4:00 PM, (D) 4:10 PM, (E) 4:30 PM
Plan
Primary tool: #8 Analyze the Units
Secondary: #7 Identify Subproblems, #3 Eliminate Possibilities
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 $2$.
Execute — Answer: B
4.OA.A.3 Step 1 Count the finished tasks
- From $1\!:\!00$ PM to $2\!:\!40$ PM, Marie has finished the first task and the second task.
- That is two equal tasks completed, not one.
💡 "Finishes the second task" means both task 1 and task 2 are over, so the clock has covered two whole tasks.
3.MD.A.1 Step 2 Measure the elapsed time
- Find how long those two tasks took by measuring the time from the start to the end.
- From $1\!:\!00$ PM to $2\!:\!40$ PM is $1$ hour and $40$ minutes, which is $100$ minutes.
💡 Adding the $60$ minutes of the full hour to the extra $40$ minutes turns the clock gap into one plain number of minutes.
4.OA.A.3 Step 3 Find minutes per task
- Split the $100$ minutes evenly between the two tasks to get the time for one task.
- This is the unit rate: minutes per task.
💡 Dividing total minutes by the number of tasks cancels "tasks" and leaves the time for a single task.
3.MD.A.1 Step 4 Add the third task
- The third task starts the moment the second one ends, at $2\!:\!40$ PM, and also takes $50$ minutes.
- Add $50$ minutes to $2\!:\!40$ PM: $20$ minutes reach $3\!:\!00$ PM, and $30$ more reach $3\!:\!30$ PM.
💡 Carrying the minutes past the next hour mark adds one more $50$-minute task onto the clock, landing on $3\!:\!30$ PM.
4.OA.A.3 From $1\!:\!00$ PM to $2\!:\!40$ PM, Marie has finished the first task and the s 3.MD.A.1 Find how long those two tasks took by measuring the time from the start to the e 4.OA.A.3 Split the $100$ minutes evenly between the two tasks to get the time for one tas 3.MD.A.1 The third task starts the moment the second one ends, at $2\!:\!40$ PM, and also Review
Reasonableness: Check the whole run: three tasks at $50$ minutes each is $150$ minutes $= 2$ hours $30$ minutes. Starting at $1\!:\!00$ PM and adding $2$ hours $30$ minutes gives $3\!:\!30$ PM, matching $\textbf{(B)}$. Tool #3 (Eliminate Possibilities) catches the traps: treating $2\!:\!40$ PM as the end of one task gives $100$ minutes per task and the late answers; dividing $100$ by $3$ instead of $2$ gives about $33$ minutes per task, which does not land on any clean choice. The trap of reading "second task" as a single task is exactly what the close choices are testing.
Alternative: Use a number line for the clock (Tool #1, Draw a Diagram). Mark $1\!:\!00$ PM and $2\!:\!40$ PM, and cut that span into two equal blocks of $50$ minutes; each block is one task. Draw a third identical $50$-minute block starting at $2\!:\!40$ PM, and its right end sits at $3\!:\!30$ PM. Seeing three equal blocks makes the answer visible without any division written down.
CCSS standards used (min grade 4)
3.MD.A.1Tell and write time, and solve problems involving addition and subtraction of time intervals in minutes (Measuring the elapsed time from $1\!:\!00$ PM to $2\!:\!40$ PM as $100$ minutes and adding $50$ minutes to $2\!:\!40$ PM to reach $3\!:\!30$ PM.)4.OA.A.3Solve multistep word problems with whole numbers using the four operations (Recognizing two tasks are done by $2\!:\!40$ PM and dividing $100$ minutes by $2$ tasks to get $50$ minutes per task before extending to the third task.)
⭐ Finishing the "second" task means two tasks are done, so split the time between two, not three.
⭐ Finishing the "second" task means two tasks are done, so split the time between two, not three.
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