In a flight of 6000km an aeroplane reduced its speed by 400 km/hr and as result the time increased by 30 minutes.find the actual speed

Question

Explain the question 

Answer 1

 6000 = R*T

 

         = (R-400)*(T+1/2)

 

 

   RT = RT + R/2 - 400T - 200

 

  0 = R/2 - 400T - 200

 

200 = R/2 - 400T

 

400  = R - 800T

 

R = 800T + 400 <--- please label this equation ALPHA

 

 

6000 = (800T + 400)T

 

6000 = (400) (2T+1)T

 

15 = (2T+1)T

 

  0 = 2T^2 + T - 15

 

0 = (   2T   -    5 )( T    +    3  )

 

T+3=0  results in negative time

 

 

T = 5/2

 

By equation ALPHA in bold above: R = 800(5/2) + 400 = 4000/2 + 400 = 2000 + 400 = 2400

 

CHECK:

 

    2400*5/2 = 1200*5 = 6000

 

   Speed reduced by 400 and time increased by 1/2;

   2000*(5/2+1/2) = 2000*3 = 6000

 

Yes it checks

 

The actual speed is 2400 km/hr for 2 and 1/2 hours