Question

The distance between a town and a mill is 30 km. A man started to walk from the mill to the town at 6:30 am while a cyclist left the town for the mill at 6:40 am, riding at a speed of 18 km/h. The man met the cyclist after walking 6km. Determine at what time the met and the man's speed.

Answer 1

Diagram is attached

Speed of the cycliest=18Km/h
Distance he traveled=(30-6)Km   [∵Total distance was 30Km and the man                                         =24Km            meet him after he traveled 6Km]
Time = Distace/Speed
         = 24/18
         = 4/3 or 1hour 20minutes
Cycliest meet the man after 1hr 20min but the man started 10 min earlier
So time taken by the man to meet the cycliest is 1hr 20 min +10 min

∴Time taken by the man=1hr 30 min or 9/6hours
   Distance traveled by the man =6Km
∴Speed of man=(6÷9/6)km/h
                         =4km/h (Ans)
Time at which they meet =Time when man begun his journey + Time taken                                                                                     him to travel 6 Km.
                                        =6:30am+1:30
                                        =8:00am (Ans)