While boarding an aeroplane a passenger got hurt The Pilot showing promptness and concern , made an arrangement to hospital the injured injured and so the plane started late by 30 minutes to reach the destination 1500 km away in time the pilot increases the speed by 100 km per hour find the original speed of the plane.
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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.
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