P. T. Usha and Shelly John decide to run a marathan between ramnagar and jamnagar. Both start
from ramnagar at 1 pm. On the way are two towns: ramgarh and rampur seprated by a distance of 15
km .P. T. Usha reaches ramgarh in 90 minutes running at a constant speed of 40 km/hr, she takes
additional 30 minutes to reach rampur. Between rampur and jamnagar she maintains at average
speed of V km/hr. Shelly John being a professional marathon runner, maintains a constant speed of 18
km/hr.they both reach jamnagar togethar after n hours. What could be the total time taken by P. T. Usha ??

• 
  
  P.T.Usha took 90 min to reach Ramnagar with a speed of 40 km/hr
  
  i.e. P.T.Usha travels 60 km (distance between Ramnagar and Ramgarh)
  
  Time taken by her from Ramgarh to Rampur = 30 min
  
  From Rampur to Jamnagar she maintains a constant speed of V km/hr
  
  (where V is a whole nos)
  
  Let N be the total time taken by P.T.Usha and Shelly John to travel from Ramnagar to
  
  Jamnagar
  
  (where N is a whole nos)
  
  Speed of Shelly John = 18 km/hr
  
  Total distance travelled by Shelly John in N hr = 18N …….(i)
  
  P.T.Usha took 2 hr to reach from Ramnagar to Rampur.
  
  She took (N-2) hr to travel from Rampur to Jamnagar with a speed of V km/hrTherefore distance between Rampur to Jamnagar = (N-2)V km
  
  Total distance = 60km + 15km + (N-2)V km = 75 + (N-2)V ….(ii)
  
  Equating both equations;
  
  18N = 75 + (N-2)V
  
  or V = 18N -75 / (N - 2)
  
  a) For N = 5 ; we get V = 5 (a whole nos)
  
  b) For N = 15; we get V = 13 (a whole nos)
  
  c) For N = 41; we get V = 17 (a whole nos)
  
  ANS. D) All of above
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• 2hr+(18n-75/v)hr
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