while boarding an aeroplane, a passenger got hurt The pilot, showing promptness and concern, made arrangements to hospitalise the - Maths -

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 min To reach the
destination, 1500 km away, in time, the pilot increased the speed
by 100km/hr Find the original speed /hr of the plane

Gursheen kaur. · Accepted Answer

Let the usual speed of the plane = x km/hr.

Increased speed of the plane = (x +100) km/hr

Time taken to reach the destination at usual speed, $t_{1} = (\frac{1500}{x}) hr$

Time taken to reach the destination at increased speed, $t_{2} = (\frac{1500}{x + 100}) hr$

Given:

t ₁ – t ₂ = 30 min

$∴ \frac{1500}{x} - \frac{1500}{x + 100} = \frac{30}{60} \Rightarrow \frac{1500 x + 150000 - 1500 x}{x (x + 100)} = \frac{1}{2} \Rightarrow x^{2} + 100 x = 300000 \Rightarrow x^{2} + 100 x - 300000 = 0 \Rightarrow x^{2} + 600 x - 500 x - 300000= 0 \Rightarrow x (x + 600) - 500 (x + 600) = 0 \Rightarrow (x + 600) (x - 500) = 0 E i t h e r x + 600 = 0 o r x - 500 = 0 \Rightarrow x = - 600 or x = 500 ∴ x = 500 (∵ Speed cannot be negative)$

Thus, the usual speed of the plane=500 km/hr.