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**mathsgal17** a car a van a truck and a bike are all travelling in the same direction on the same road each at its own constant speed. At 10am the car overtakes the van; at noon it overtakes the truck; at 2pm it overtakes the bike. At 4pm the truck overtakes the bike and at 6pm the van overtakes the truck

a) the speed of the car is 120km/h and the speed of the truck is 80km/h

i) Find the speeds of the van and the bike.

ii) find the time at which the van overtakes the bike

b) Let c and T represent the speeds in km/h of the car and the truck respectively.

i) Find the speeds of the van and the bike in terms of c and T

ii) Show that the time when the van overtakes the bike is the same regardless of the speeds of the car and the truck