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At 6am, just after the racing club opens, Martha begins to jog around

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kritisachan
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At 6am, just after the racing club opens, Martha begins to jog around [#permalink] New post   Updated on: 26 Jun 2023, 01:00
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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

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E

Originally posted by kritisachan on 26 Jun 2023, 00:59.
Last edited by Bunuel on 26 Jun 2023, 01:00, edited 1 time in total.
Renamed the topic.
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Re: At 6am, just after the racing club opens, Martha begins to jog around [#permalink] New post   26 Jun 2023, 04:50
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kritisachan wrote:
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

Posted from my mobile device


  • Speed of Martha = 6000m / hr
  • Speed of Saad = 8000m / hr

By 6:30 am, Martha covers 3000 m.

Number of laps completed by Martha = \(\frac{3000}{600}\) = 5 laps.

At 6:30 am, both Martha and Saad are the starting point. Saad has to complete at least 10 laps.

Distance to be covered by Saad = 10 * 600 m

Relative Speed = 8000 - 6000 = 2000 m/hr

Time taken = \(\frac{6000}{2000}\) = 3 hours

Hence, Saad will complete 10 laps at 9:30 am.

Option E
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Re: At 6am, just after the racing club opens, Martha begins to jog around [#permalink] New post   02 Jul 2023, 18:27
kritisachan wrote:
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?


Martha
0.6 km at 6 km/h
1 round in 6 min
10 rounds in 60 min

Also Martha has a head start of 5 rounds (Started at 6:00)

Saad
0.6 km at 8 km/h
1 round in 4.5 min
40/3 rounds in 60 min

\((40/3-10)x-5=5\)
\(x=3\) hours

Hence, Saad would have done 5 more rounds than Martha at 9:30 AM.

Option (E)
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Re: At 6am, just after the racing club opens, Martha begins to jog around [#permalink] New post   04 Jul 2023, 19:18
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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At 6am, just after the racing club opens, Martha begins to jog around [#permalink] New post   06 Jul 2023, 22:26
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kritisachan wrote:
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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At 6am, just after the racing club opens, Martha begins to jog around [#permalink]
06 Jul 2023, 22:26
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