Two cars start from the same point at the same time towards the same destination which is 420 km away. The first and second car travel at respective speeds of 60 kmph and 90 kmph. After travelling for sometime the speed s of the two cars get interchanged. Finally the second car reaches the destination one hour earlier than the first. Find the time after which the speeds get interchanged?

• Try it this way..
  car A at 60 kmph :___60___|___120___|__180___|__240___|__300___|__360__|__420__|
  car B at 90 kmph :___90___|___180___|__270___|__360___|__450___|
  
  Our destination is only 420km.
  So now the interchanging speeds such that car B reaches 1 hour less than car A,
  
  Car A now at 90kmph aftr 240km: ___60___|___120___|__180___|__240___|__(240+90=330)___|__(330+90=20)__|
  
  Car B now at 60kmph after 360km: ___90___|___180___|__270___|__360___|__(360+60=420)___|
  
  So from figure car B reaches one hour less than car A.
  So from the figure car B reaches
  
• 11 years agoHelpfull: Yes(38) No(2)
• first A & B travels x hours
  after exchange A travels y+1 hours and B travels y hours
  A speed 60
  B speed 90
  60x+90(y+1)=420 eq--->1
  90x+60y=420 eq--->2
  by solving eq---> 1&2
  60x+90(y+1)=90x+60y
  30x-30y=90
  form this x=4,y=1
  the speeds are exchanged after 4 hours...
  
• 11 years agoHelpfull: Yes(33) No(0)
• let the speed be interchanged after 'k' hrs
  A B
  distance covered in 'k' hrs(km) 60k 90k
  remaining distance(km) 420-60k 420-90k
  new speed(kmph) 90 60
  time to cover remaining distance (420-60k)/90--->slow (420-90k)/60---->fast
  
  slow - fast = 1
  (420-60k)/90 - (420-90k)/60 = 1
  on solving we get
  25k-70=30
  25k=100
  k=4----->(ans)
  
• 11 years agoHelpfull: Yes(18) No(0)
• hi rudra....for 1st 4 hrs A covers 240km and B covers 360km...if their speeds get interchanged after this A still need 2hrs to cover remaining(180 km) and B needs 1hr to cover remaining distance(60km)...therefore B covers 1hr earlier than A...
  
• 11 years agoHelpfull: Yes(9) No(0)
• let after travelling X km they interchange their speeds.
  Ta=(X/60) + (420-X)/90 ...........1
  Tb=(X/90) + (420-X)/60 ...........2
  a/c Ta=Tb+1 ......................3
  after solving we get X=50 km
  time at which they inter change their speeds = X/60 = 50/60 = 5/6 hrs
  
  
• 11 years agoHelpfull: Yes(6) No(7)
• near about 2 hours
• 11 years agoHelpfull: Yes(3) No(5)
• Why this Kolaveri D?
  
  Time taken by Ist car = 420/60=7hrs
  Now let after T hours the speeds get interchanged.
  So for Ist car:
  Distance traveled in T hours with 60KPH + Distance traveled in (6-T)hours with 90 KPH speed = 420
  60T+90(6-T)=420
  Solve it for T. You will get T=4hours
  Note : I have taken 6-T because the total time(7) was reduced by 1Hr.
• 11 years agoHelpfull: Yes(3) No(3)
• speed gets interchahged after the end of 4th hour...
• 11 years agoHelpfull: Yes(1) No(2)
• Edit*
  Try it this way..
  car A at 60 kmph :___60___|___120___|__180___|__240___|__300___|__360__|__420__|
  car B at 90 kmph :___90___|___180___|__270___|__360___|__450___|
  
  Our destination is only 420km.
  So now interchanging speeds such that car B reaches 1 hour less than car A,
  
  Car A now at 90kmph aftr 240km: ___60___|___120___|__180___|__240___|__(240+90=330)___|__(330+90=20)__|
  
  Car B now at 60kmph after 360km: ___90___|___180___|__270___|__360___|__(360+60=420)___|
  
  So from figure car B reaches one hour less than car A.
• 11 years agoHelpfull: Yes(1) No(0)
• let speed get interchanged after X hr.
  (420-60x)/90=(420-90x)/60)+1
  after solving we get x=4
  
• 9 years agoHelpfull: Yes(1) No(0)
• Let the total time taken by the cars be a and b
  Let the time after which the speed is interchanged be t
  For car A, 60t+90(a-t) = 420, 90a - 30t = 420 .......(1)
  For car B, 90t + 60(b-t) = 420, 60b + 30t = 420 ....(2)
  Using both (1) and (2), we get 90a + 60b = 840
  But as a - b =1, 90a + 60(a-1) = 840.
  Solving a = 6.
  Substituting in equation 1, we get t = 4
  
• 9 years agoHelpfull: Yes(1) No(0)
• If measured by distance then, after travelling 300 Km, the speed of the cars was interchanged.
  Anybody have an idea about the time ? pl. explain
  
• 11 years agoHelpfull: Yes(0) No(0)
• after 4 hours speeds get interchanged
  
• 11 years agoHelpfull: Yes(0) No(1)
• @priyadharshini plzzz explain in detail
• 11 years agoHelpfull: Yes(0) No(0)
• @priyadharshini Hi...I got it.....thank u very much
• 11 years agoHelpfull: Yes(0) No(0)
• can anyone plz explain it to me wid full solution
• 11 years agoHelpfull: Yes(0) No(0)
• Let the total time taken by the cars be a and b
  Let the time after which the speed is interchanged be t
  For car A, 60t+90(a-t) = 420, 90a - 30t = 420 .......(1)
  For car B, 90t + 60(b-t) = 420, 60b + 30t = 420 ....(2)
  Using both (1) and (2), we get 90a + 60b = 840
  But as a - b =1, 90a + 60(a-1) = 840.
  Solving a = 6.
  Substituting in equation 1, we get t = 4
• 9 years agoHelpfull: Yes(0) No(0)
• After 4 hours..
• 9 years agoHelpfull: Yes(0) No(0)
• Let the total time taken by the cars be a and b Let the time after which the speed is interchanged be t For car A, 60t+90(a-t) = 420, 90a - 30t = 420 .......(1) For car B, 90t + 60(b-t) = 420, 60b + 30t = 420 ....(2) Using both (1) and (2), we get 90a + 60b = 840 But as a - b =1, 90a + 60(a-1) = 840. Solving a = 6. Substituting in equation 1, we get t = 4
• 9 years agoHelpfull: Yes(0) No(0)