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

The Correct Option is A

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