Question

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 original speed of the plane be x km/hr.

If the speed of the plane is reduced by 100 km/hr, then

Reduced speed of the plane = (x − 100) km/hr

Time taken by the plane to reach its destination at original speed, `t_1=2800/xhr`

Time taken by the plane to reach its destination at reduced speed, `t_1=2800/(x-100)hr`

Given,

Time taken by the plane to reach its destination at reduced speed − Time taken by the

plane to reach its destination at original speed = 30 minutes

`t_2-t_1=1/2hr`

`rArr 2800/(x-100)-2800/x=1/2`

`rArr(2800x-2800(x-100))/(x(x-100)=1/2`

`rArr2800xxx100xx2=x^2-100x`

`rArrx^2-100x-560000=0`

`rArrx^2-800x+700x-560000=0`

`rArrx(x-800)+700(x-800)=0`

`rArr(x-800)(x+700)=0`

`rArrx-800=0` or `x+700=0`

`rArrx=800` or `x=-700`

`thereforex=800`  `therefore`[Speed cannot be negative]

Original speed of flight = 800 km/hr

∴ Original duration of flight, `t_1=2800/800`

`=7/2`

`=3(1)/2 Hrs`

Thus, the original duration of the flight is 3 hours 30 minutes.