1. **State the problem:** We need to find how much energy a racing cyclist must ingest to produce a mechanical power output of 200 watts for 3 hours and 20 minutes, given that the biological yield (efficiency) is 25%. 2. **Understand the given data:** - Power output, $P = 200$ watts - Time, $t = 3$ hours 20 minutes = $3 + \frac{20}{60} = 3.333$ hours - Biological yield (efficiency), $\eta = 25\% = 0.25$ - 1 watt = 1 joule/second - 1 kcal = 4200 joules 3. **Calculate total mechanical energy output:** Mechanical energy output $E_{mech} = P \times t$ in joules. Convert time to seconds: $$t = 3.333 \times 3600 = 12000 \text{ seconds}$$ So, $$E_{mech} = 200 \times 12000 = 2,400,000 \text{ joules}$$ 4. **Calculate total energy ingested:** Since only 25% of ingested energy converts to mechanical energy, $$E_{mech} = \eta \times E_{ingested} \Rightarrow E_{ingested} = \frac{E_{mech}}{\eta}$$ $$E_{ingested} = \frac{2,400,000}{0.25} = 9,600,000 \text{ joules}$$ 5. **Convert ingested energy to kcal:** $$E_{ingested} = \frac{9,600,000}{4200} \approx 2285.7 \text{ kcal}$$ 6. **Final answer:** The cyclist needs to ingest approximately 2,300 kcal to produce 200 watts for 3 hours and 20 minutes. This matches the first option: approx. 2,300 kcal.