A and B run a 1000 m race. if A gives B a start of 50 m, A wins by 14 sec. If B gives A start of 22 sec B wins By 20 m. Find time taken by A to complete the race.

• case 1: A (dist)= 1000;
  A (time)= t1;
  B (distance) = 950;
  B(time) = t1+14
  and
  case 2:
  A(dist)= 980;
  A(time)= t2;
  B(dist)=1000;
  B(time)= t2+22;
  then,
  speed of A= 1000/t1=980/t2
  = t2= 980*t1/1000 -----(1)
  and
  speed of B= 950/(t1+14)=1000/(t2+22) ------(2)
  put eq (1) in eq (2)
  we get t1=100sec
  
• 11 years agoHelpfull: Yes(27) No(8)
• @pritesh according to the question B gives A a start of 22sec.so dont u thnk that in case 2 velocity of B shld be 1000/(t2-22)?plz let me knw if i am wrng...
• 11 years agoHelpfull: Yes(8) No(0)
• Let speed of A and B be a and b m/sec.
  Time taken to cover 1000m by A = 1000/a
  Time taken to cover 950m by B = 950/b
  Now 950/b - 1000/a = 14 - Eqn 1
  
  Also 980/a + 22 = 1000/b,
  1000/b - 980/a = 22 - Eqn 2
  
  Let 1/a = x and 1/b=y,
  950y - 1000x = 14 and
  1000y - 980x = 22
  
  Solving, x=1/10 and a = 1/x =10m/s
  Time taken by A to run 1km = 1000/10 = 100 seconds.
  
• 11 years agoHelpfull: Yes(8) No(0)
• distance time
  case 1: A - 1000 t1
  B - 950 t1+14
  case 2: A - 980 t2
  B - 1000 t2+22
  now,
  speed of A= 1000/t1=980/t2
  = t2= 980*t1/1000 -----(1)
  and
  speed of B= 950/(t1+14)=1000/(t2+22) ------(2)
  put eq (1) in eq (2)
  we get t1=100sec
• 11 years agoHelpfull: Yes(5) No(0)
• 100 Sec.
• 11 years agoHelpfull: Yes(3) No(3)
• Let speed of a and b are A and B resp..
  case 1
  time taken by a=1000/A SEC.
  time taken by b=(1000/A)+14(In 950mt.)
  distance equation for b
  [(1000/A)+14]*B+50=1000
  so, b=950/[(1000/A)+14]......(1)
  case 2
  time taken by a=22+980/A
  distance equation for b
  [22+980/A]*B=1000
  [22+980/A]*{950/[(1000/A)+14]}=1000
  [22+980/A]/[(1000/A)+14]=20/19
  A=10m/s
  time taken by a=1000/10=100sec.
  
  
• 11 years agoHelpfull: Yes(2) No(0)
• Case 2 : When B = 1000 m , A = 980m and B wins by 22 sec
  i.e. A takes 22 sec to complete 50 m
  i.e. A completes 1 m in 22/20 = 1.1sec
  thus 1000 m in 1.1 * 1000 = 100 sec
• 11 years agoHelpfull: Yes(2) No(1)
• a/b=1000/950-14b=980/1000-22b
  after solving we get b=8.33
  1000/950-14(8.33)=x/8.33
  after solving,
  we get
  x=10
  so,finally 1000/10
  that is,100 is ans.
• 11 years agoHelpfull: Yes(2) No(0)