In a flight of 2800 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 100 km/hr and time of flight increased by 30 minutes. What was the original average speed of the aircraft?
- A. 700\text{ km/hr}
- B. 750\text{ km/hr}
- C. 800\text{ km/hr} ✓
- D. 900\text{ km/hr}
Correct Answer: C. 800\text{ km/hr}
Explanation
Let original speed be v and time be t. We know vt = 2800. With reduced speed, (v-100)(t+0.5) = 2800. Substituting t = \frac{2800}{v} gives (v-100)(\frac{2800}{v} + 0.5) = 2800. Solving the quadratic equation v^2 - 100v - 560000 = 0 yields (v-800)(v+700) = 0, making v = 800\text{ km/hr}.
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