Sticking 'A' Key: Continue, Switch Machines, or Report
Twelve minutes into a 30-minute typewriting test, you have typed 240 words with 6 errors. For the last three minutes the 'a' key on your machine has been sticking: it fails to print about one stroke in five unless you strike it much harder. Your speed has fallen from 34 to 18 gross words per minute, and you have already had 9 failed 'a' strokes. A spare machine is available at the front of the hall. Moving to it, transferring your sheet, and checking alignment would take about 5 minutes; after that you could work at 34 words per minute with about 2 errors per 100 words. If you stay, you estimate 24 words per minute with about 6 errors per 100 words. The marking rule deducts 5 words per error. You have 18 minutes left. The invigilator has not yet noticed your difficulty.
1. Calculate the net output for the remaining 18 minutes under staying versus switching. Which is better, and by how much?
Read the worked answer
Staying: 24 gross wpm × 18 min = 432 gross words. At 6 errors per 100 words, expected errors = 432 × 0.06 = 25.92, or about 26 errors. Deduction = 26 × 5 = 130 words. Net from remaining time = 432 − 130 = 302 net words.
Switching: 5 minutes are lost to moving and alignment, leaving 13 minutes of typing. 34 gross wpm × 13 min = 442 gross words. At 2 errors per 100 words, expected errors = 442 × 0.02 = 8.84, or about 9 errors. Deduction = 9 × 5 = 45 words. Net from remaining time = 442 − 45 = 397 net words.
Switching is better by about 95 net words (397 − 302). The extra gross words are not the main reason: the decisive factor is that the error rate falls from 6 per 100 to 2 per 100, so the deduction shrinks sharply. You should also report the faulty key to the invigilator immediately, because a machine fault is an exam-hall matter and may need to be recorded. However, the calculation assumes the transfer preserves your existing 240 words. If transferring the sheet risks losing or misaligning the first page, the comparison changes completely: losing 240 gross words (about 210 net after the 6 existing errors) would make staying safer.
2. What if the move and alignment check would take 9 minutes rather than 5? Recalculate and decide. What general threshold does this reveal?
Read the worked answer
With a 9-minute move, only 9 minutes of typing remain after switching. Gross words = 34 × 9 = 306. Expected errors = 306 × 0.02 = 6.12, or about 6 errors. Deduction = 6 × 5 = 30 words. Net = 306 − 30 = 276 net words.
Staying remains at 302 net words, so staying is now better by 26 net words. The general threshold is found by setting the switching net equal to the staying net. Staying produces about 302 net words. Switching produces 34 × (18 − t) × 0.90 net words, because the 5-word deduction per error at a 2% error rate removes 10% of gross output. So 30.6 × (18 − t) = 302 gives 18 − t ≈ 9.9, or t ≈ 8.1 minutes. If the move takes less than about 8 minutes, switch; if it takes more, stay. The judgement is not 'a spare machine is always better' but a comparison of lost time against reduced error deductions. In either case, tell the invigilator about the sticking key so the fault is documented.