In a flight of 2800 km, an aircraft was slowed down due to bad weather. It's average speed is reduced by 100km/hr and time increased by 30 minutes. Find the original duration of the flight
Answers
Answer:
Original duration of the flight = 3 hours 30 minutes
Step-by-step explanation:
We will be using:
Speed = Distance / Time
Distance = Speed * Time
Time = Distance / Speed
Units:
Distance: km
Speed: km per hour
TIme: hours
Given:
Distance = 2800 km
Original speed = S ; New speed = S - 100
Original time = t ; New time = (t + 0.5)
As the aircraft is covering the same distance, we have:
Original Speed * Original Time = New Speed * New Time
=> St = (S - 100)(t + 0.5)
=> St = St + 0.5S - 100t - 50
=> 0 = S/2 - 100t - 50 ..............(∵ 0.5S = S/2)
=> S/2 - 100t - 50 = 0
=> S - 200t - 100 = 0
S = Distance / time = 2800/t
=> (2800/t) - 200t - 100 = 0
=> 2800 - 200t² - 100t = 0
=> 28 - 2t² - t = 0 ...........(Dividing throughout by 100)
=> 2t² + t - 28 = 0 .........(Multiplying throughout by -1)
=> 2t² + 8t - 7t - 28 = 0
=> 2t(t + 4) - 7(t + 4) = 0
=> (2t - 7)(t + 4) = 0
=> t = 7/2 or t = -4
But "t" being time cannot be negative
=> t = 7/2 = 3.5
Original time is 3.5 hours
=> Original time = 3 hours 30 minutes
Check:
Distance = 2800 km
Original time = 3.5 hours
Original speed = 800 km per hour
New time = 3.5 + 0.5 = 4 hours
Distance = 2800 km
Speed = 2800 / 4 = 700 km per hour
We can see that speed has dropped by 100 km per hour √