Dara ran on a treadmill that had a readout indicating the time remaining in her exercise session. When the readout...

1. Translate the problem requirements: The treadmill shows 'time remaining' (not elapsed time). When 10% is completed, 90% remains with 24 min 18 sec showing. We need to find what displays when 40% is completed (60% remains).
2. Find the total exercise duration: Use the fact that 24 min 18 sec represents 90% of the total session to calculate the full session length.
3. Calculate remaining time at 40% completion: Determine what time corresponds to the remaining 60% of the session and convert to minutes and seconds format.
4. Match with answer choices: Compare the calculated result with the given options to identify the correct answer.

Execution of Strategic Approach

1. Translate the problem requirements

Let's start by understanding what's actually happening here. Dara is on a treadmill that shows a countdown timer - it displays how much time is LEFT in her workout, not how much time has passed.

Think of it like a kitchen timer counting down. When she's 10% done with her workout, the timer shows 24 minutes and 18 seconds remaining. This means she still has 90% of her workout left to go.

We need to find what the timer will show when she's 40% complete. At that point, she'll have 60% of her workout remaining.

Process Skill: TRANSLATE - Converting the problem language about 'readout indicating time remaining' into clear mathematical understanding.

2. Find the total exercise duration

Here's the key insight: if 24 minutes 18 seconds represents 90% of her total workout time, we can find the complete workout duration.

Let's convert 24 minutes 18 seconds to just seconds first:

• 24 minutes = \(24 \times 60 = 1,440\) seconds
• Plus 18 seconds = \(1,440 + 18 = 1,458\) seconds

Now, if 1,458 seconds represents 90% of the total workout:

• 90% of total = 1,458 seconds
• 1% of total = \(1,458 \div 90 = 16.2\) seconds
• 100% of total = \(16.2 \times 100 = 1,620\) seconds

So her complete workout is 1,620 seconds long.

3. Calculate remaining time at 40% completion

When Dara has completed 40% of her workout, she has 60% remaining.

Time remaining = 60% of total workout time
Time remaining = 60% of 1,620 seconds
Time remaining = \(0.60 \times 1,620 = 972\) seconds

Now let's convert 972 seconds back to minutes and seconds:

• \(972 \div 60 = 16\) minutes with remainder
• \(972 - (16 \times 60) = 972 - 960 = 12\) seconds

So the readout will show 16 minutes 12 seconds.

4. Match with answer choices

Our calculated answer is 16 minutes 12 seconds.

Looking at the answer choices:

1. 10 min 48 sec
2. 14 min 52 sec
3. 14 min 58 sec
4. 16 min 6 sec
5. 16 min 12 sec

Our answer matches choice E exactly.

Final Answer

The correct answer is E. 16 min 12 sec.

This makes sense because as Dara completes more of her workout (from 10% to 40%), the remaining time shown on the readout decreases (from 24 min 18 sec to 16 min 12 sec).

Common Faltering Points

Errors while devising the approach

1. Misinterpreting the countdown timer concept
Many students miss that the treadmill shows a countdown timer displaying time REMAINING, not time elapsed. They incorrectly assume 24 min 18 sec represents the time Dara has already exercised (10% of total), rather than understanding it represents the time left (90% of total). This fundamental misunderstanding leads to setting up the wrong equation entirely.

2. Confusing completion percentages with remaining percentages
Students often struggle to translate between 'percentage completed' and 'percentage remaining.' They may correctly understand the countdown concept but then incorrectly think that at 40% completion, 40% of time remains (instead of 60%), leading to wrong calculations throughout the problem.

Errors while executing the approach

1. Time conversion arithmetic errors
Converting between minutes/seconds and total seconds involves multiple steps. Students commonly make errors like: incorrectly calculating 24 × 60 (getting 1,440 wrong), forgetting to add the 18 seconds, or making division errors when converting 972 seconds back to 16 minutes and 12 seconds.

2. Percentage calculation mistakes
When calculating 1,458 ÷ 90 to find 1% of the total workout, students may get decimal handling wrong (getting something other than 16.2), or make errors in the subsequent multiplication by 100. These small arithmetic mistakes compound to give incorrect final answers.

Errors while selecting the answer

1. Selecting answers with similar time values
Answer choices D (16 min 6 sec) and E (16 min 12 sec) are very close, differing by only 6 seconds. Students who make minor arithmetic errors in the final conversion step may get 16 minutes correct but miscalculate the seconds, leading them to choose D instead of the correct answer E.