Q. 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?

  Soln :- let  the original speed of the plane u.

t1=1500/u

t2=1500/(u+100)

t2=t1-(30/60) =t1-1/2

According to Question,

t2=t1-(30/60) =t1-1/2

1500/(u+100) =(1500/u)-1/2

(1/2)=(1500/u)-1500/(u+100)

(1/2) =[1500(u+100)-1500u]/u(u+100)

(1/2) =[1500u+1500-1500u]/u(u+100)

(1/2) =[1500]/u(u+100)

u(u+100)=3000

u^2+100u-3000=0

u={-100 ± √[(100)^2-4×1×(-3000)]}/2

u={-100 ± √[(10000+1200000]}/2

u={-100 ± √[1210000]}/2

u={-100 ± 1100}/2

for +ve 

u={-100 +1100}/2 

u={1000}/2 

u=500

-ve value is not valid 

so the original speed of the plane=500 km/h