Math, asked by sreelakshmi2107, 10 months ago

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

Answered by venupillai
7

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 √

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