Tortoise travels uniformly 20 km a day. The hare, starting from the same point three days later to overtake the tortoise, travels at the uniform rate of 15 km the first day, at a uniform rate of 19 km the second day, and so forth in arithmetic progression. After how many days does the hare catches up with the tortoise?

• In 3 days , tortoise has covered 60 kms distance.
  In next 2 days, the distance between hare and tortoise has increased to 60+5+1= 66 kms.
  From 6 th day, distance is being reduced. First day 3 kms, next day .. 7 kms and so on.
  If hare catches tortoise after n+5 days from start of tortoise , then
  66 = (n/2)*(2*3+(n-1)*4)
  
  solving it, we get
  n=5.5
  
  so hare will catch tortoise on 8th day when it starts running after tortoise.
• 11 years agoHelpfull: Yes(3) No(1)
• after 3 days tortoise will cover 60km,
  now hare starts its journey(4 day of tortoise)
  Arithmetic progression=15,19,23,27,.....(15+4(n-1))
  day 1:hare covers 15km tortoise covers :(60+20)=80km
  day 2:h:(15+19)=34 t:100
  day 3:h:(34+23)=57 t:120
  day 4:h:(57+27)=74 t:140
  day 5:h:(74+31)=105 t:160
  day 6:h:(105+35)=140 t:180
  day 7:h:(140+39)=179 t:200
  day 8:h:(179+43)=222 t:220
  so,hare catches tortoise in 8 days.......
• 11 years agoHelpfull: Yes(3) No(0)