One day Vijay was out bicycling. After entering a one-way tunnel and after having ridden one-fourth of the distance through it, he looked back over his shoulder and saw a bus approaching the tunnel entrance at a speed of 80 miles/hr. Doing a quick mental exercise, Vijay realized that if he accelerated immediately to his top speed, he could just escape with his life, whichever direction he rode. What is Vijay's top biking speed in miles/hr?

a) 32 (b) 36 (c) 40 (d) 48 (e) none of these

• 40
  
  s be the speed of the bike, d be the length of tunnel and x be distance of bus (B) from tunnel mouth
  
  by the time bus travels distance x, bike travels d/4 so, (d/4)/(x/80) = s
  so, s=20d/x -------I
  also, by the time bike travels 3d/4, bus travels x=d so, s = (3d/4)/((d+x)/80)
  so, s=60d/(d+x)------II
  
  Now I and II are equal.
  Hence solving it, we get
  x=d/2
  
  now, bike travels d/4 when bus travels d/2 so ratio of speeds of bus and bike =(d/4)/(d/2)
  
  hence, speed of the bike = 80/2 = 40 mph
  
  
• 13 years agoHelpfull: Yes(4) No(1)