A car starts from town A towards town B. Another car starts from town B towards town A at the same time. The pass each other 64km from town B. Both cars continued on their journey after passing each other. When they reach the respective towns, they turn around, back to where they came from. This time, they pass each other 52km from town A. What is the distance between town A & B?

• let speed of car A is a km/hr and B is b km/hr and total distance is D.
  Now, for 1st part,
  64/b = (D-64)/a ....(1)
  for 2nd part,
  (D+52)/b = (D+(D-52))/a ....(2)
  divide (1) by (2) and on solving we get
  D = 140Km.
• 10 years agoHelpfull: Yes(28) No(0)
• Let d = distance from a to b
  :
  A --------------------d-----------------------B
  car a>--------(d-64)------*-----64------< car b
  :
  First time they meet:
  car a travels (d-64) km
  car b travels 64 km
  :
  2nd meeting
  car b>----52-------*--------(d-52)------< car a
  :
  car a travels 64 + (d-52) = (d+12)
  car b travels (d-64) + 52 = (d-12)
  :
  The ratio a:b of the distances traveled by the two cars remain the same; therefore:
  1st meeting = 2nd meeting
  %28d-64%29%2F64 = %28d%2B12%29%2F%28d-12%29
  ;
  
  Cross multiply
  (d-64)(d-12) = 64(d+12)
  d^2 - 12d - 64d + 768 = 64d + 768
  ;
  Subtract 768 from both sides, arrange as a quadratic equation
  d^2 - 76d - 64d = 0
  d^2 - 140d = 0
  ;
  Factor
  d(d - 140) = 0
  ;
  Two solutions
  d = 0
  and
  d = 140 km distance between the towns
• 10 years agoHelpfull: Yes(5) No(2)
• 64/x = (z-64)/y ....(1)
  for 2nd part,
  (z+52)/y = (z+(z-52))/x ....(2)
  divide (1) by (2) and on solving we get
  z = 140Km.
• 10 years agoHelpfull: Yes(1) No(0)