A computer is downloading a file of 120 megabytes. The download proceeds at a constant rate of 15 megabytes per...

1. TRANSLATE the problem information

• Given information:
  • File size: 120 megabytes (MB)
  • Download rate: 15 megabytes per second (MB/s)
  • Find: time in seconds to download the entire file

2. INFER the mathematical approach

• This is a rate problem using the formula: \(\mathrm{Rate \times Time = Total\:Amount}\)
• Since we know the rate and total amount, we need to solve for time
• Rearrange the formula: \(\mathrm{Time = \frac{Total\:Amount}{Rate}}\)

3. SIMPLIFY by substituting and calculating

• \(\mathrm{Time = \frac{120\:MB}{15\:MB/s}}\)
• \(\mathrm{Time = 8\:seconds}\)

Answer: A (8)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students recognize they have rate and total amount but choose the wrong operation to combine them. Instead of dividing total by rate, they might add, subtract, or multiply the numbers.

• Adding: \(\mathrm{120 + 15 = 135}\) → Choice C (135)
• Subtracting: \(\mathrm{120 - 15 = 105}\) → Choice B (105)
• Multiplying: \(\mathrm{120 \times 15 = 1800}\) → Choice D (1800)

The Bottom Line:

Rate problems require understanding that to find time, you must divide the total amount by the rate. Students who memorize the formula \(\mathrm{Rate \times Time = Total}\) but struggle to rearrange it algebraically will often guess at operations, leading to systematic wrong answers that match the available choices.