NMOS 2010 Prelim round Q15

Town A and Town B are 12 km apart. At 10 a.m., Tom and Harry travelled towards each other from Town A and Town B respectively. Tom walked at a speed of 20 m/min for 2 minutes after every 10 minutes of running at 165 m/min. Harry took a 4 minutes rest after each 15 minutes of running at 165 m/min. What time did they meet each other? [2 marks]


Tom
 Distance (m)


      1650     40          1650       40           1650        40    330
|-----------|------|--------------|------|---------------|------|------|--------?
0            10     12                 22     24                 34     36    38
Time (min)


Harry
165 x 15 = 2475 m


Distance (m)
           2475                  0                2475                    0
|----------------------|--------|----------------------|------------|---------?
0                         15          19                          34               38
Time (min)


1650 x 3 + 40 x 3 + 330 = 5400 m


2475 x 2 = 4950 m


5400 + 4950 = 10350 m


12000 - 10350 = 1650 m


1650 /(165+165) = 5 min


38 + 5 = 43 min

               43 min
   |--------------------|
10 am                10.43 am

It was 10.43 a.m.