There are two towers A and B. Their heights are 200ft and 150ft respectively and the foot of the towers are 250ft apart. Two birds on top of each tower fly down with the same speed and meet at the same instant on the ground to pick a grain. What is the distance
between the foot of tower A and the grain?

• Let a = 200 = height of Tower A
  Let g = the number of feet from the base of Tower A to the grain.
  The distance flown by Bird A is:
  √(200² + g²)
  
  Let b = 150 = height of Tower B
  Since the distance between the bases of the towers is 250 feet, and "g" is the distance from the base of Tower A to the grain, the distance from the base of Tower B to the grain is (250 - g).
  The distance flown by Bird B is:
  √[150² + (250 - g)²]
  
  Since they arrived at the same time and traveled at the same speed, the two distances are equal.
  
  √(200² + g²) = √[150² + (250 - g)²]
  Squaring both sides,
  200² + g² = 150² + (250 - g)²
  40000 + g² = 22500 + (62500 - 500g + g²)
  40000 + g² = 85000 - 500g + g²
  Adding (-g² + 500g - 40000) to both sides,
  500g = 45000
  g = 45000 / 500 = 90
  
  The grain is 90 feet from the bottom of Tower A.
• 10 years agoHelpfull: Yes(9) No(0)
• Since there speed is same and time to reach the grain is also same.
  Therefore there distance is different.
  As s1=d1/t and s2=d2/t
  since s1=s2,
  therefore d1=d2
  d1^2=x^2 + 200, d2^2=(250-x)^2 + 150^2
  solving the eq you will get the ans. (250-x)^2+150^2=x^2+200^2
  ans is 90ft
• 11 years agoHelpfull: Yes(6) No(2)