An army 50 miles long marches at a constant rate. A courier standing at the rear moves forward and delivers the message to the first person and then turns back and reaches the rear of the army as the army completes 50 miles. Find the distance travelled by the courier.

• Let the speed of the army be x and speed of the courier be y. The time taken by the courier to reach the first person be t1 and to return be t2.
  
  (y-x)t1 = 50--------(i)
  (y+x)t2 = 50---------(ii)
  x(t1+t2) = 50---------(iii)
  
  from (iii):t1+t2=50/x-------(iv)
  from (ii):t2=50/y+x-------(v)
  from (iii):t1=50/y-x-------(vi)
  
  Putting (v) & (vi) in (iv):50/x=(50/y-x)+(50/y+x) ------> 1/x=(1/y+x)+(1/y-x)----->
  Solving y=(1+2^.5)x=(1+1.414)x=2.414x
  
  Now distance travelled by courier =(t1+t2)*y = (50/x) * 2.414x
  = 50*2.414=120.7 mile
  
  
  hence 120.7 mile
• 12 years agoHelpfull: Yes(2) No(0)