A faucet dispenses water at a constant rate of 2~liters every 15~seconds. At this rate, how long will it take...

1. TRANSLATE the problem information

• Given information:
  • Rate: 2 liters every 15 seconds
  • Target volume: 18 liters
  • Need to find: time to fill container

2. INFER the solution approach

• This is a constant rate problem - we can solve it multiple ways:
  • Find unit rate (time per 1 liter) then scale up
  • Count how many 2-liter portions fit in 18 liters, then multiply by time per portion

3. SIMPLIFY using unit rate method

• If 2 liters take 15 seconds, then 1 liter takes: \(\mathrm{15 ÷ 2 = 7.5}\) seconds
• For 18 liters: \(\mathrm{18 × 7.5 = 135}\) seconds

Answer: C (135 seconds)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misinterpret the rate and think "15 liters every 2 seconds" instead of "2 liters every 15 seconds"

They might calculate: \(\mathrm{18 ÷ 15 = 1.2}\), then \(\mathrm{1.2 × 2 = 2.4}\) seconds, or get confused trying to make sense of their setup. This leads to confusion and abandoning systematic solution, causing them to guess among the answer choices.

Second Most Common Error:

Inadequate SIMPLIFY execution: Students set up the problem correctly but make arithmetic errors

For example, they might calculate \(\mathrm{15 ÷ 2 = 6.5}\) instead of 7.5, leading to \(\mathrm{18 × 6.5 = 117}\) seconds. Since 117 isn't an answer choice, they might round to the closest option and select Choice B (120).

The Bottom Line:

The key challenge is correctly interpreting the rate relationship and maintaining accuracy through multi-step arithmetic calculations.