Question

The play started late by 30 minutes to reach the destination 1500 km away in time the pilot increase the speed by 100 km per hour find the original speed of the plane

Answer 1

uploaded 2 solution
one for competitive exam purpose and second for board exam purpose.

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.