Three runners A, B and C run a race, with runner A
finishing 12 meters ahead of runner B and
18 meters ahead of runner C, while runner B finishes 8 meters ahead of
runner C. Each runner travels the entire distance at a constant speed.What was the length of the race?

(1)
36 meters

(2)
48 meters


(3)
60 meters

(4)
72 metersPlease explain ur answer.

1) 36 meters
2) 48 meters
3) 60 meters
4) 72 meters

• let distance is D
  than first time: At1=D,
  Bt1=D-12
  Ct1=D-18
  Now Second time: Bt2=D
  Ct2=D-8
  Now taking Ratio of above equations we have
  t1/t2=(D-12)/D=(D-18)/(D-8)
  i.e. D=48
• 10 years agoHelpfull: Yes(1) No(1)
• let the total distance=x meter
  time taken by A to complete the race=t1
  time taken by B to complete the race=t2
  time taken by C to complete the race=t3
  now according to the question:-
  total distance covered by B when A completed the race is
  (x/t2)*t1
  total distance covered by C when A completed the race is
  (x/t3)*t1
  total distance covered by C when B completed the race is
  (x/t3)*t2
  B lags behind A by 12 meter so,
  x-(x/t2)*t1=12..........(1)
  C lags behind A by 18 meter so,
  x-(x/t3)*t1=18..........(2)
  C lags behind B by 8 meter so,
  x-(x/t3)*t2=8.............(3)
  now,
  solving equation 1st we get t2/t1=x/(x-12)........(4)
  solving equation 2nd we get t3/t1=x/(x-18)........(5)
  solving equation 3rd we get t3/t2=x/(x-8)...........(6)
  solving equation 4th and 5th we get
  t2/t3=(x-18)/(x-12)........(7)
  solving equation 6th and 7th we get
  (x-18)/(x-12)=(x-8)/x
  finally we get the value of x=48
  so the totla distance of the race is 48 meters
  
• 9 years agoHelpfull: Yes(1) No(0)