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Bismuth83
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Two runners, Alex and Bella, are training on a circular track. Alex co Updated on: 08 Apr 2025, 09:53
Originally posted by Bismuth83 on 21 Jan 2025, 12:12.
Last edited by Bunuel on 08 Apr 2025, 09:53, edited 1 time in total.
Edited the wording.
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Time to Lap: 6 Laps Completed: 4
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25% (medium)

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80% (02:08) correct 20% (02:31) wrong based on 350 sessions

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Two runners, Alex and Bella, are training on a circular track. Alex completes one lap every 90 seconds, while Bella completes one lap every 120 seconds. They both start at the same point at the same time and run continuously in the same direction.

Based on the above information, select for Time to Lap the number of minutes it takes for Alex to complete exactly one more lap than Bella, and for Laps Completed the number of laps Alex will have completed by that time.
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Time to Lap: 6 Laps Completed: 4
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Two runners, Alex and Bella, are training on a circular track. Alex co 08 Apr 2025, 09:53
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Official Solution:
Bunuel

Two runners, Alex and Bella, are training on a circular track. Alex completes one lap every 90 seconds, while Bella completes one lap every 120 seconds. They both start at the same point at the same time and run continuously in the same direction.

Based on the above information, select for Time to Lap the number of minutes it takes for Alex to complete exactly one more lap than Bella, and for Laps Completed the number of laps Alex will have completed by that time.



Time to Lap Laps Completed
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4
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Alex completes 1 lap every 90 seconds. In that time, Bella completes 90/120 = 3/4 of a lap.

This means Alex gains 1/4 of a lap on Bella every 90 seconds. To gain a full lap, Alex would need 4 intervals of 90 seconds, which is 4 * 90 = 360 seconds, or 6 minutes.

Since Alex runs 1 lap every 90 seconds, in 360 seconds he runs 360/90 = 4 laps.


Correct answer:

Time to Lap "6"

Laps Completed "4"
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Two runners, Alex and Bella, are training on a circular track. Alex co 21 Jan 2025, 21:47
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"Lap" mean to overtake another person by a full lap in a race.

LCM of 90,120 => 360
=> Alex take 360 sec => 6 min

2. rounds Alex take => 360/90 = 4 rounds
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Two runners, Alex and Bella, are training on a circular track. Alex co 22 Jan 2025, 07:00
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1. The question asks us to basically find the point when Alex laps Bella.

2. Alex runs at a speed of \(\frac{1 \ lap}{90 \ seconds} = \frac{1}{90}\) of a lap per second, while Bella runs at a speed of \(\frac{1 \ lap}{120 \ seconds} = \frac{1}{120}\) of a lap per second .

3. Alex gains \(\frac{1}{90} - \frac{1}{120} = \frac{30}{90 * 120} = \frac{1}{360}\) of a lap per second. That means it will take Alex \(\frac{1}{\frac{1}{360}} = 360\) seconds or 6 minutes to gain a lap ahead.

4. The number of laps Alex does in 6 minutes is equal to \(\frac{1}{90} * 360 = 4\).

5. Our answer will be: 6 and 4.
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Two runners, Alex and Bella, are training on a circular track. Alex co 14 Feb 2025, 19:34
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Two runners, Alex and Bella, are training on a circular track. Alex completes one lap every 90 seconds, while Bella completes one lap every 120 seconds. They both start at the same point at the same time and run continuously in the same direction.

Based on the above information select for Lapped Time the time it takes for Alex to lap Bella in minutes and for Number of Laps the number of laps Alex completes by that time.

In 90 seconds, Alex completes a lap and Bella completes 90/120 lap = 3/4 lap.

So, every 90 seconds, Alex completes 1/4 lap more than Bella.

So, to complete a 1 lap more than Bella, and thus "lap" Bella, Alex takes 1/(1/4) × 90 seconds = 4 × 90 seconds = 360 seconds.

360 seconds = 6 minutes

For the first column, select 6.

Since we already know that Alex runs for 4 × 90 seconds to lap Bella and that Alex runs 1 lap in 90 seconds, we know that, in lapping Bella, Alex completes 4 laps.

For the second column, select 4.

Correct answer: 6, 4
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