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kritisachan
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At 6am, just after the racing club opens, Martha begins to jog around Updated on: 26 Jun 2023, 01:00
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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Difficulty:

65% (hard)

Question Stats:

65% (02:56) correct 35% (03:06) wrong based on 135 sessions

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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
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At 6am, just after the racing club opens, Martha begins to jog around 26 Jun 2023, 04:50
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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

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  • 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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At 6am, just after the racing club opens, Martha begins to jog around 02 Jul 2023, 18:27
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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?
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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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At 6am, just after the racing club opens, Martha begins to jog around 04 Jul 2023, 19:18
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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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At 6am, just after the racing club opens, Martha begins to jog around 06 Jul 2023, 22:26
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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
Show more

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 07 Jun 2026, 02:34
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Martha speed: 6000m/h
Saad speed: 8000m/h
Martha travels 3000m between 6 am to 6:30 am.

Since we need to find the time Saad takes to travel 5 more laps than Martha, we would need to account for the meters she has already traveled before Saad shows up.

Let ‘t’ be the number of hours it takes for Saad to travel 5 more laps than Martha.

Equation: 600 merers x 5 laps = 8000t - (6000t + 3000)
3000 is for the meters Martha has already covered.
After solving the equation: t = 3hours

So from 6:30 am, it takes exactly 3 hours for Saad to travel 5 more laps than Martha.

6:30am + 3hours = 9:30 am

Option E
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At 6am, just after the racing club opens, Martha begins to jog around 07 Jun 2026, 07:06
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To achieve the goal, he must first make up that 3km deficit just to tie her AND then run an additional 3km to get his 5-lap lead.
= 5 * 600 + 3000 (because in 1hr Martha covers 6 km, so in 1/2 an hr she covers 3 km)
= 6000 m
= 6km

Time taken by Saad = 6 km/(their relative speed = 2 km/hr)
= (6 / 2) hr
= 3 hr
So, time = 6:30 + 3 hr = 09:30 AM
Ans E

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

Posted from my mobile device
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