Question

The distance between two towns A and B is360km.A minibus left town A at 8.15a.m and travelled towards B at an average speed of 90km/hr. A matatu left town B at 10.35a.m on the same day and travelled towards A at an average speed of 110km/hr.

1.  
   1. how far from A did they meet? 
   2. at what time did the two vehicles meet?
2. A motorist left his home at 10.30a.m on the same day and travelled at an average speed of 100km/hr. He arrived at B at the same time as minibus. Calculate the distance from B to his home. 

Answer 1

1.  
   1. 
      
      Distance travelled by minibus when matatu leaves B
      90 × 2¹/₃ = 90 × ⁷/₃ =210km
      R.d = 360 − 210 =150
      R.s = 90 + 110 = 200
         t = 150 ×60 =45mins
               200
      Distance minibus has travelles = 90 × 3⁵/₆₀
                 =90 × 185 =277.5km
                             60
   2. 10.35
      + .45
      11.20
      =11:20am
2. Time minibus reached B
   360  = 4hrs
    90
   8.15 + 4 = 12.15pm
   Time motorist took = 12.15
                                  −10.30
                                      1.45
                               =1hr 45mins
   d= 100 × 1⁴⁵/₆₀ 
     =100 × 1³/₄ 
     =100 × ⁷/₄ =175km