Question

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. 

Answer 1

1. 
   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