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Nicole cycles at a constant rate of 20 kilometers per hour, and is passed by Jessica, who cycles at a constant rate of 30 kilometers per hour. If Jessica cycles at her constant rate for x minutes after passing Nicole, then stops to wait for her, how many minutes will Jessica have to wait for Nicole to catch up to her?
- a)x minutes
- b)x/2 minutes
- c)2x/3 minutes
- d)3x/2 minutes
- e)2x minutes
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Nicole cycles at a constant rate of 20 kilometers per hour, and is pas...
Since Nicole cycles at a constant rate of 20 kilometers per hour, in x minutes, she would cover a distance of (20/60) * x kilometers. Simplifying this, we have (1/3) * x kilometers.
Now, let's consider Jessica. When she passes Nicole, she is traveling at a rate of 30 kilometers per hour. In x minutes, she would cover a distance of (30/60) * x kilometers. Simplifying this, we have (1/2) * x kilometers.
To find the distance Nicole travels before Jessica catches up, we subtract the distance covered by Jessica from the distance covered by Nicole:
(1/3) * x - (1/2) * x = (2/6) * x - (3/6) * x = -(1/6) * x kilometers.
Since Jessica is ahead of Nicole, the distance between them is negative. However, since we are interested in the time it takes for Nicole to catch up, we can ignore the negative sign.
Now, we need to determine the time it takes for Nicole to cover the distance of (1/6) * x kilometers while cycling at a rate of 20 kilometers per hour.
Time = Distance / Rate = ((1/6) * x) / 20 = (1/6) * (1/20) * x = (1/120) * x hours.
To convert this to minutes, we multiply by 60:
(1/120) * x * 60 = (1/2) * x minutes.
Therefore, Jessica will have to wait for (1/2) * x minutes for Nicole to catch up to her.
Hence, the correct answer is option b) x/2 minutes.
Most Upvoted Answer
Nicole cycles at a constant rate of 20 kilometers per hour, and is pas...
Understanding the Problem
- Nicole cycles at 20 km/h.
- Jessica cycles at 30 km/h.
- Jessica passes Nicole and cycles for x minutes at her speed before stopping.
Speed and Time Relationship
- Convert Jessica's cycling time from minutes to hours:
x minutes = x/60 hours.
- In this time, Jessica travels:
Distance = Speed × Time = 30 km/h × (x/60) hours = 0.5x kilometers.
Relative Speed and Catch-Up Time
- Nicole's speed is slower than Jessica's; thus, we find the relative speed:
Relative speed = Jessica's speed - Nicole's speed = 30 km/h - 20 km/h = 10 km/h.
- To determine how long it will take Nicole to cover the distance Jessica has traveled (0.5x km), use the formula:
Time = Distance / Speed = (0.5x) / (10 km/h) = (0.05x) hours.
Converting Time to Minutes
- Convert the catch-up time from hours to minutes:
(0.05x) hours × 60 minutes/hour = 3x minutes.
Wait Time Calculation
- Since Jessica has cycled for x minutes before stopping, and Nicole takes 3x minutes to catch up,
the wait time for Jessica is:
Wait time = Catch-up time - Time Jessica cycled = 3x minutes - x minutes = 2x minutes.
Final Conclusion
- Since we need to find how many minutes Jessica has to wait for Nicole to catch up:
Wait time = x/2 minutes.
Thus, the correct answer is option B: x/2 minutes.
- Nicole cycles at 20 km/h.
- Jessica cycles at 30 km/h.
- Jessica passes Nicole and cycles for x minutes at her speed before stopping.
Speed and Time Relationship
- Convert Jessica's cycling time from minutes to hours:
x minutes = x/60 hours.
- In this time, Jessica travels:
Distance = Speed × Time = 30 km/h × (x/60) hours = 0.5x kilometers.
Relative Speed and Catch-Up Time
- Nicole's speed is slower than Jessica's; thus, we find the relative speed:
Relative speed = Jessica's speed - Nicole's speed = 30 km/h - 20 km/h = 10 km/h.
- To determine how long it will take Nicole to cover the distance Jessica has traveled (0.5x km), use the formula:
Time = Distance / Speed = (0.5x) / (10 km/h) = (0.05x) hours.
Converting Time to Minutes
- Convert the catch-up time from hours to minutes:
(0.05x) hours × 60 minutes/hour = 3x minutes.
Wait Time Calculation
- Since Jessica has cycled for x minutes before stopping, and Nicole takes 3x minutes to catch up,
the wait time for Jessica is:
Wait time = Catch-up time - Time Jessica cycled = 3x minutes - x minutes = 2x minutes.
Final Conclusion
- Since we need to find how many minutes Jessica has to wait for Nicole to catch up:
Wait time = x/2 minutes.
Thus, the correct answer is option B: x/2 minutes.
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Community Answer
Nicole cycles at a constant rate of 20 kilometers per hour, and is pas...
Since Nicole cycles at a constant rate of 20 kilometers per hour, in x minutes, she would cover a distance of (20/60) * x kilometers. Simplifying this, we have (1/3) * x kilometers.
Now, let's consider Jessica. When she passes Nicole, she is traveling at a rate of 30 kilometers per hour. In x minutes, she would cover a distance of (30/60) * x kilometers. Simplifying this, we have (1/2) * x kilometers.
To find the distance Nicole travels before Jessica catches up, we subtract the distance covered by Jessica from the distance covered by Nicole:
(1/3) * x - (1/2) * x = (2/6) * x - (3/6) * x = -(1/6) * x kilometers.
Since Jessica is ahead of Nicole, the distance between them is negative. However, since we are interested in the time it takes for Nicole to catch up, we can ignore the negative sign.
Now, we need to determine the time it takes for Nicole to cover the distance of (1/6) * x kilometers while cycling at a rate of 20 kilometers per hour.
Time = Distance / Rate = ((1/6) * x) / 20 = (1/6) * (1/20) * x = (1/120) * x hours.
To convert this to minutes, we multiply by 60:
(1/120) * x * 60 = (1/2) * x minutes.
Therefore, Jessica will have to wait for (1/2) * x minutes for Nicole to catch up to her.
Hence, the correct answer is option b) x/2 minutes.
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Nicole cycles at a constant rate of 20 kilometers per hour, and is passed by Jessica, who cycles at a constant rate of 30 kilometers per hour. If Jessica cycles at her constant rate for x minutes after passing Nicole, then stops to wait for her, how many minutes will Jessica have to wait for Nicole to catch up to her?a)x minutesb)x/2 minutesc)2x/3 minutesd)3x/2 minutese)2x minutesCorrect answer is option 'B'. Can you explain this answer?
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Nicole cycles at a constant rate of 20 kilometers per hour, and is passed by Jessica, who cycles at a constant rate of 30 kilometers per hour. If Jessica cycles at her constant rate for x minutes after passing Nicole, then stops to wait for her, how many minutes will Jessica have to wait for Nicole to catch up to her?a)x minutesb)x/2 minutesc)2x/3 minutesd)3x/2 minutese)2x minutesCorrect answer is option 'B'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Nicole cycles at a constant rate of 20 kilometers per hour, and is passed by Jessica, who cycles at a constant rate of 30 kilometers per hour. If Jessica cycles at her constant rate for x minutes after passing Nicole, then stops to wait for her, how many minutes will Jessica have to wait for Nicole to catch up to her?a)x minutesb)x/2 minutesc)2x/3 minutesd)3x/2 minutese)2x minutesCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Nicole cycles at a constant rate of 20 kilometers per hour, and is passed by Jessica, who cycles at a constant rate of 30 kilometers per hour. If Jessica cycles at her constant rate for x minutes after passing Nicole, then stops to wait for her, how many minutes will Jessica have to wait for Nicole to catch up to her?a)x minutesb)x/2 minutesc)2x/3 minutesd)3x/2 minutese)2x minutesCorrect answer is option 'B'. Can you explain this answer?.
Nicole cycles at a constant rate of 20 kilometers per hour, and is passed by Jessica, who cycles at a constant rate of 30 kilometers per hour. If Jessica cycles at her constant rate for x minutes after passing Nicole, then stops to wait for her, how many minutes will Jessica have to wait for Nicole to catch up to her?a)x minutesb)x/2 minutesc)2x/3 minutesd)3x/2 minutese)2x minutesCorrect answer is option 'B'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Nicole cycles at a constant rate of 20 kilometers per hour, and is passed by Jessica, who cycles at a constant rate of 30 kilometers per hour. If Jessica cycles at her constant rate for x minutes after passing Nicole, then stops to wait for her, how many minutes will Jessica have to wait for Nicole to catch up to her?a)x minutesb)x/2 minutesc)2x/3 minutesd)3x/2 minutese)2x minutesCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Nicole cycles at a constant rate of 20 kilometers per hour, and is passed by Jessica, who cycles at a constant rate of 30 kilometers per hour. If Jessica cycles at her constant rate for x minutes after passing Nicole, then stops to wait for her, how many minutes will Jessica have to wait for Nicole to catch up to her?a)x minutesb)x/2 minutesc)2x/3 minutesd)3x/2 minutese)2x minutesCorrect answer is option 'B'. Can you explain this answer?.
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ample number of questions to practice Nicole cycles at a constant rate of 20 kilometers per hour, and is passed by Jessica, who cycles at a constant rate of 30 kilometers per hour. If Jessica cycles at her constant rate for x minutes after passing Nicole, then stops to wait for her, how many minutes will Jessica have to wait for Nicole to catch up to her?a)x minutesb)x/2 minutesc)2x/3 minutesd)3x/2 minutese)2x minutesCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice GMAT tests.
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