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A bus left Makindu at 11.45 a.m and traveled towards Mombasa at an average speed of 80km/h. A Nissan Matatu left Makindu at 1.15 p.m on the same day and traveled along the same road at an average speed of 120km/hr. The distance between Makindu and Mombasa is 400km.

  1. Determine the time of the day the Nissan overtook the bus. 
  2. Both vehicles continue towards Mombasa at their original speeds. Find how long the Matatu had to wait at Mombasa before the bus arrived. 

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  1. Nissan and bus distance speed and time
    Speed of bus = 80km/hr
    Nissan
    Dept - 1:15pm
    Speed of nissan = 120km/hr
      13:15
    11:45
        1:30 - Time
    Distance covered by bus before nissan started
    D = S × T
    D = 80 × 1.5
    D = 120km
    T. taken by Nissan to catch up with the bus
    R.S = 120 − 80
          =40km/h
    T.T = Distance btwn  =   120km
                  R.S                     40km/h
                                   =3 hours
    Time of day was:
     1315
    + 300
     1615hrs or 4:15 p.m
  2. After 3 hours, Bus = 80 × 3
                               = 240 + 120
                               =360km (from Makindu)
    ∴ T. Taken by bus to reach Mombasa:
     T= D = 40 = 0.5hrs = 30mins
          S     80
    T. Taken by Nissan:
    T= D = 40  = 0.3hrs = 20mins
         S    120
    30min − 20min
    =10mins

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