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, in time, the pilot increased the speed by 100 km/hour. Find the original speed of the plane.
Do you appreciate the values shown by the pilot, namely promptness in providing help to the injured and his efforts to reach in time?

Answer 1

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
$\frac{1500}{x}$ = $\frac{1500}{x+100}$+ $\frac{1}{2}$
$\frac{1500}{x}$ - $\frac{1500}{x+100}$ = $\frac{1}{2}$
$\frac{1500(x+100)-1500x}{x(x+100)}$= $\frac{1}{2}$
$\frac{1500x+1500\times 100-1500x}{x^2+100x}$ = $\frac{1}{2}$
$\frac{1500\times 100}{x²+100x}$ = $\frac{1}{2}$
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.

The value depicted by the pilot here are humanity.