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Martha ran for 3.5 hours at a speed of 6 km/h. So she covered a total distance of 21 km = 35 laps.
Saad ran for 3 hours at a speed of 8 km/h. So he covered a total distance of 24 km = 40 laps.

Since Saad is ahead of Martha by 5 laps at the end of both their runs, answer is 9:30.

Of course this approach worked better because the question exactly asks 5 laps. Had it asked when Saad would be 2 or 3 laps ahead, then any of the above methods would be better.
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kritisachan
At 6am, just after the racing club opens, Martha begins to jog around a 600-metre racing track at a steady pace of 6 kilometres an hour. Saad arrives later and only begins running at 6:30am, maintaining a steady pace of 8 kilometres per hour. If they both started their runs at the same point, and continue to run until at least 9:30am, by what time has Saad done five more laps around the track than Martha?

A. 7:30am
B. 8:10am
C. 8:30am
D. 9:10am
E. 9:30am

Solution:

  • Let us look at this question from a different perspective and use the options to our advantage.
  • Martha runs at 6 kmph which means \(\frac{6000}{600}=\) 10 laps in 1 hour
  • Saad runs at 8 kmph which means \(\frac{8000}{600}=\) 13.33 laps in 1 hour

  • It is clear that at 6:30am -
    • Martha = 5 laps
    • Saad = 0 laps

  • 1 hour later at 7:30am -
    • Martha = 5 + 10 = 15 laps
    • Saad = 0 + 13.33 = 13.33 laps
  • Saad is behind

  • 2 hours later at 8:30am -
    • Martha = 15 + 10 = 25 laps
    • Saad = 13.33 + 13.33 = 26.66 laps
  • Saad is 1.66 laps ahead

  • 3 hours later at 9:30am -
    • Martha = 25 + 10 = 35 laps
    • Saad = 26.66 + 13.33 = 40 laps
  • Saad is 5 laps ahead

Hence the right answer is Option E
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