A rehearsal studio is reserved for 3 hours 50 minutes for a band's practice session. The band spends 14 minutes...

1. TRANSLATE the problem information

• Given information:
  • Total reservation: 3 hours 50 minutes
  • Setup time: 14 minutes
  • Pack-up time: 8 minutes
  • Each song: 6 minutes
• Find: Maximum number of full song rehearsals

2. TRANSLATE time units to be consistent

• Convert total time to minutes: 3 hours 50 minutes = \(3 \times 60 + 50 = 230\) minutes
• Now all times are in the same units

3. INFER what time is actually available for songs

• The setup and pack-up are required and take away from song time
• Available time for songs = Total time - Setup - Pack-up
• Available time = \(230 - 14 - 8 = 208\) minutes

4. SIMPLIFY to find how many songs fit

• Each song takes 6 minutes, so divide available time by song length
• \(208 \div 6 = 34\) remainder 4 (use calculator if needed)
• This means 34 full songs with 4 minutes left over

5. APPLY CONSTRAINTS to select final answer

• Since the question asks for "full song rehearsals," we cannot count partial songs
• The 4 remaining minutes are not enough for another full 6-minute song
• Maximum number of full songs = 34

Answer: B. 34

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students forget to convert hours to minutes or mix up units partway through the calculation.

They might calculate 3 hours 50 minutes as 3.50 hours or work with mixed units (some calculations in hours, others in minutes). This leads to incorrect intermediate results and ultimately wrong final answers. This may lead them to select a choice that doesn't match any of the given options, causing confusion and guessing.

Second Most Common Error:

Poor INFER reasoning: Students don't realize they need to subtract setup and pack-up time first before calculating songs.

They might divide the total 230 minutes by 6 directly, getting \(230 \div 6 = 38.33\), then round down to 38. This may lead them to select Choice (D) (36) after some additional confusion about the extra time needed.

The Bottom Line:

This problem tests your ability to work systematically through a multi-step time management scenario. The key insight is recognizing that fixed overhead times (setup/pack-up) must be handled separately from the variable activity time (songs), and that real-world constraints mean partial activities don't count toward the final answer.