In a flight of 600 km, an aircraft was slowed due to bad weather. Its average speed for the trip was reduced to 200 km/hr and time of flight increased by 30 minutes. Find the original duration of flig

Question

In a flight of 600 km, an aircraft was slowed due to bad weather. Its average speed for the trip was reduced to 200 km/hr and time of flight increased by 30 minutes. Find the original duration of flight.

Accepted Answer

Step 1: Let the speed of aircraft be $x$ km/hr.
$\frac{600}{x - 200} - \frac{600}{x} = \frac{30}{60}$
Step 2: $\Rightarrow x^2 - 200x - 240000 = 0$
$(x - 600)(x + 400) = 0$
Step 3: $x = 600$ (rejecting $x = -400$).
Speed of aircraft $= 600$ km/hr.
Duration of flight $= \frac{600}{600} = 1$ hr.

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