Question

In a flight of 3000 km, an aircraft was slowed down by bad weather. Its average speed for the trip was reduced by 100 km/hour and the time increased by one hour. Find the original duration of the flight.

• A. 5 hours
• B. 6 hours
• C. 4 hours
• D. 10 hours

Answer 1

Answer: (A)

5 hours

Answer 2

Assume the initial speed be $x\ \frac{km}{hr}$

the new speed will be $(x - 100)\ \frac{km}{hr}$

Assume the duration of flight be $t\ hours$

actual time taken be $(t - 1 )\ hours$

So, the total distance will be $x \times t = 3000$ – (i)

As we know that, Speed is inversely proportional to time,

= $\frac{x}{x - 100} = \frac{t + 1}{t}$

= $xt = xt + x - 100t - 100$

$x - 100t = 100$

$\frac{3000}{t} - 100t = 100$

= $-100t^2 - 100t + 3000 = 0$

= $t^2 + t - 30 = 0$

=$(t + 6)(t - 5) = 0$

So, the value of $t$ can be -6 and 5

So, the time taken cannot be negative then $t = 5\ hours$

The correct option is (A): 5 hours