Math, asked by ibnagaraj28, 9 months ago

A plane taken 30 min lease for journey of 1500 km if speed is increased by 100km/h from the usual speed . find the it speed​

Answers

Answered by ButterFliee
2

GIVEN:

  • A plane taken 30 min least for journey of 1500 km.
  • Its speed is increased by 100km/h from the usual speed.

TO FIND:

  • What is the actual speed of the plane ?

SOLUTION:

Let the actual speed of plane be 'x' km/hr

CASE:- 1)

For the journey of 1500 km, the time taken will be:-

\bf{\dfrac{1500}{x} = t_1}

CASE:-2)

if speed is increased by 100km/h from the usual speed

\bf{\dfrac{1500}{x+100} = t_2}

According to question:-

\sf{\longmapsto t_1 - t_2 = \dfrac{30}{60} }

\sf{\longmapsto \dfrac{1500}{x} - \dfrac{1500}{x+100} = \dfrac{1}{2}}

\sf{\longmapsto \dfrac{ 1500(x+10) - 1500x}{x(x+100)} = \dfrac{1}{2} }

\sf{\longmapsto \dfrac{\cancel{1500x }+ 15000 - \cancel{1500x} }{x^2 + 100x} = \dfrac{1}{2} }

\sf{\longmapsto 15000 \times 2 = x^2 + 100x }

\sf{\longmapsto 30000 = x^2 + 100x }

\sf{\longmapsto 0 = x^2 + 100x - 30000}

\sf{\longmapsto 0 = x^2 +(600-500)x -30000 }

\sf{\longmapsto 0= x^2 +600x -500x -30000 }

\sf{\longmapsto 0= x(x +600) - 500(x + 600)  }

\sf{\longmapsto 0= (x+600)(x-500) }

\bf{\longmapsto x= -600  } ( Speed can't be in negative )

\bf{\longmapsto x = 500 }

Hence, the speed of the plane is 500 km/hr

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