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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 increased by 30 min. Find the original duration of the flight.

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3 \frac{1}{2} hours

4 \frac{1}{2} hours

5 \frac{1}{2} hours

2 \frac{1}{2} hours

answer is A.

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Detailed Solution

Suppose, original speed =x km/hr.
Now, time of flight

= \frac{2800}{x} hours

New speed

= (x - 100) km / hr

Time of flight for new speed

= \frac{2800}{x - 100} hours

Now, time increased by 30 min. Thus,

\frac{2800}{(x - 100)} - \frac{2800}{x} = \frac{30}{60}

\frac{1}{2} = \frac{2800 x - 2800 (x - 100)}{x (x - 100)}

x^{2} - 100 x - 560000 = 0

x^{2} - 800 x + 700 x - 560000 = 0

x (x - 800) + 700 (x - 800) = 0

(x - 800) (x + 700) = 0

x - 800 = 0 x + 700 = 0

x = 800, - 700

Neglect negative value.
Thus, original speed x= 800 km/hr.
Time of flight for original speed

T = \frac{2800}{800}

T = 3 \frac{1}{2} hours

.
Correct option is 1

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