Multiple choice

In a flight of 2,800 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?

  1. 700 km/hr

  2. 750 km/hr

  3. 800 km/hr

  4. 900 km/hr
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let original speed be v. 2800/v - 2800/(v-100) = -0.5. Solving this quadratic: 2800(v-100) - 2800v = -0.5v(v-100). -280000 = -0.5v^2 + 50v. v^2 - 100v - 560000 = 0. (v-800)(v+700) = 0. v = 800.

AI explanation

Let the original speed be x km/hr, making the delayed speed (x - 100) km/hr. Using the formula Time equals Distance divided by Speed, the difference in time is 2800/(x - 100) - 2800/x = 0.5 hours. Multiplying by 2x(x - 100) gives 5600x - 5600x + 560000 = x^2 - 100x, which simplifies to x^2 - 100x - 560000 = 0. Factoring this quadratic equation yields (x - 800)(x + 700) = 0. Since speed must be positive, the original speed was 800 km/hr.

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