Speed P6

A car and a motorcycle set off from Green Town and Pink Town respectively at the same time. The car, travelling at a constant speed, took 10 hours to reach Pink Town. The motorcycle, travelling at a constant speed, took 6 hours to reach Green Town. The vehicles passed by each other when they were 218 3/4 km from Pink Town. Find
a) the distance between the two towns and
b) the speed of the car.


C: 10 h --> 1 distance
      1 h --> 1/10 distance

M: 6 h --> 1 distance
      1 h --> 1/6 distance

Total: 1 h --> 1/10 + 1/6 = 4/15 distance
4/15 distance --> 1 h
15/15 distance --> 15/4 x 1 = 3.75 h

3.75 h --> 218 3/4 km
6 h --> 6/3.75 x 218 3/4= 350 km

a) The distance between the two towns was 350 km.

350/10 = 35 km/h

b) The speed of the car was 35 km/h.


Alternative method

For constant distance, SC : SM = TM : TC     (S = D/T)
(total distance)                          = 6 : 10
                                                 = 3 : 5

For constant time, DC : DM = SC : SM          (D = S x T)
(when they met)                   = 3 : 5

5 u --> 218 3/4 km

8 u --> 8/5 x 218 3/4 = 350 km

a) The distance between the two towns was 350 km.


350/10 = 35 km/h

b) The speed of the car was 35 km/h