An aeroplane files along the four sides of a square at the speeds of 200,400,600 and 800km/hr.Find the average speed of the plane around the field.

• let side of square = x and time taken to each side be t1,t2,t3,t4
  so t1=x/200 , t2=x/400, t3= x/600 t4=x/800
  total time T=t1+t2+t3+t4
  total distance D= x+x+x+x = 4x
  average speed= D/T = 4x/{(x/200) + (x/400) + (x/600) + (x/800)}
  = 400/(1/2 + 1/4 + 1/6 + 1/8)
  =(400 x 24)/(12 + 6 + 4 + 3)
  =9600/25
  =384 km/h ans
• 12 years agoHelpfull: Yes(7) No(0)
• Using 2*a*b/(a+b)..............505.2631 km/hr
• 10 years agoHelpfull: Yes(0) No(0)
• Solution:
  For such questions , where the distance covered is the same for all the speeds, the formula for 4 different speeds is
  4abcd/(abc + bcd + cda + dab)
  
  where, a,b,c,d are the different speeds to cover the same distance
  
  Therefore, average speed =
  {4(200)(400)(600)(800)}/{(200)(400)(600) + (400)(600)(800) + (600)(800)(200) + (800)(200)(400)}
  = (400)(2)(4)(6)(8)/{(2)(4)(6) + (4)(6)(8) + (6)(8)(2)+(8)(2)(4)}
  = (153600)/( 48 + 192 + 96 + 64)
  = (153600)/(240 + 160) = 384 km
• 9 years agoHelpfull: Yes(0) No(0)