Question

Q.13 In a flight of 2800 km, an aircraft was slowed down due to bad weather. Its average

speed is reduced by 100 km/h and time increased by 30 minutes. Find the original duration

of the flight.

Answer 1

Let the speed of aircraft be x km/h
Distance travelled = 2800 km
Time taken = Distance / Speed = (2800/x ) hours
Given that when the speed is reduced by 100 km/h, time is reduced by 30 min
New speed = (x – 100) km/h
That is, 30 min = 30/60 hr = (1/2) hr
Time taken after the speed was reduce = [2800/(x – 100)] hr
Hence, [2800/(x – 100)] = (2800/x) + (1/2)
[2800/(x-100)] - [2800/x] = 1/2
Hence, x2 - 100x - 560000 = 0
x2 - 800x + 700x - 560000 = 0
x(x - 800) + 700(x - 800) = 0
(x + 700) (x - 800) = 0
x = - 700 or 800
Since speed cannot be negative, x = 800
Thus original duration of the flight = 2800/800 = 7/2 hours
= 3 hr 30 mins

Answer 2

There you go.
Note that '-4' is rejected as the time cannot be a negative number.