Question

while boarding an aeroplane a passenger got hurt .the pilot showing promptness and concern made arrangements to hospitalise the injured and so the plane started late by 30 minutes.to reach the destination,1500 km away the pilot increased the speed by 100 km/h.find the original speed

Answer 1

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Answer 2

Answer:

Step-by-step explanation:

Let the Original speed of the aeroplane be x km/h.

Time taken to cover 1500 km with the usual speed of x km/h = 1500 / x hrs

Time taken to cover 1500 km with the increase speed of (x+100) km/h = 1500 / (x+100) hrs

ATQ

1500 / x = 1500 / (x+100) + ½

1500 / x -  1500 / (x+100) = ½

1500(x+100) -1500x / x(x+100)= ½

1500x + 1500 × 100 -1500x / x² +100x = ½

1500 × 100 / x² +100x = ½

2(1500 × 100 ) = x² + 100x

300000 = x² +100x

x² +100x - 300000 =0

x² -  500 x  + 600 x - 300000= 0

x(x - 500) + 600(x - 500)= 0

(x+600)  (x - 500) = 0

(x+600)  = 0  or  (x - 500) = 0

x = -600  or  x = 500

Speed cannot be negative, so x = 500

Hence the usual speed of the plane is 500 km/h.