Speed P6

Cars are travelling to and fro from Greens Town to Sins City. The cars leave the Towns at regular interval and a car will meet another car coming in the opposite direction at every 6 min. Ronald starts cycling from Greens Town to Sins City while Annie starts cycling in the opposite direction. Both leave the Towns at the same time. Ronald and Annie will meet a car coming in the opposite direction every 7 and 8 min respectively. They met each other after cycling for 56 min. What is the time taken by a car to travel from Greens Town to Sins City?

CG [ ][ ][ ][ ][ ][ ]                             Units show the respective
                            [ ][ ][ ][ ][ ][ ] CS distance travelled in the
                                                      time given in the question
R    [     7 R     ]
                         [ ][ ][ ][ ][ ][ ][ ] CS

CG [ ][ ][ ][ ][ ][ ][ ][ ]
                                   [    8 A   ] A

7 R --> 5 C

If R cycled 56 min to travel 7 R to meet CS which travelled 7 C, to travel just 5 C. CS would take 5/7 x 56 = 40 min.

8 A --> 4 C

If A cycled 56 min to travel 8 A to meet CG which travelled 8 C. to travel just 4 C, CG would take 4/8 x 56 = 28 min.

40 + 28 = 68 min

Time taken by a car to travel from Green Town to Sins City was 68 minutes.