Speed P6

A train took 12 hours to travel from Singapore to Ipoh. Its average speed for the first 1/3 of the journey was 1/2 the average speed for the remaining journey. Find the time taken for the first 1/3 of the journey.


Distance [     ][     ][     ]
Speed    1/2 S<    S    >
Time      [ ][ ]  [ ]     [ ]    12 h     [Each distance is 1 unit, so Time inversely proportional to Speed]

4 u --> 12 h
1 u --> 12 ÷ 4 = 3 h

2 u --> 2 x 3 = 6 h

The time taken for the first 1/3 of the journey was 6 h.


Alternative method
                          12 h
1/3 D     2/3 D
!-----!-----!-----!
!____!________!
 1/2 S       S

T1 = 1/3 D ÷ 1/2 S
     = 2/3 DS

T2 = 2/3 D ÷ S
     = 2/3 DS

T1 + T2 = 12 h
2/3 DS + 2/3 DS = 12 h

T1 = T2 = 12 ÷ 2 = 6 h

Time taken for the first 1/3 of the journey was 6 h.