Question

The average speed of a pick-up was 20km/h faster than the average speed of a lorry. The pick-up took 45 minutes less than the lorry to cover a distance of 180 km.  

1. If the speed of the lorry was x km/h:  
   • Write expressions in terms of x for the time taken by the lorry and the pick-up respectively to cover the distance of 180 km
   • Determine the speed of the lorry and that of the pick-up. 
2. The distance between towns A and B is 240 km. On a certain day the pick-up started from town A at 8.30 a.m. and the lorry started from town B at the same time. Determine the time that the lorry and the pick-up met. 

Answer 1

1.  
   • lorry time = ¹⁸⁰/_x km hrs
     Pick up time = ¹⁸⁰/_x+20 km hrs
                          
   • ¹⁸⁰/_x km  − ¹⁸⁰/_x+20 km = ³/₄  
      x² + 20x − 4800= 0
     (x − 60)(x + 80) = 0
                           x = 60km/h or −80km/h
                        ∴ x = 60km/h
             hence lorry = 60km/h &
                  pick up = 80km/h
2. distance pick up +distance lorry = 240km
   80(t − 8.30am) + 60 (t − 8. 30am) = 240
   where t meeting time
                  140t− 680 − 510 = 240
                                           t ≈ 1013hrs