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John and Jacob set out together on bicycle traveling at 15 and 12 miles per hour, respectively. After 40
minutes, John stops to fix a flat tire. If it takes John one hour to fix the flat tire and Jacob continues to ride during this time, how many hours will it take John to catch up to Jacob assuming he resumes his ride at 15 miles per hour? (consider John's deceleration/acceleration before/after the flat to be negligible)
minutes, John stops to fix a flat tire. If it takes John one hour to fix the flat tire and Jacob continues to ride during this time, how many hours will it take John to catch up to Jacob assuming he resumes his ride at 15 miles per hour? (consider John's deceleration/acceleration before/after the flat to be negligible)
- a)3
- b)3.33
- c)
- d)4
- e)
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
John and Jacob set out together on bicycle traveling at 15 and 12 mile...
It is easier to break this motion up into different segments. Let's first consider the 40 minutes up until John stops to fix his flat.
40 minutes is 2/3 of an hour.
In 2/3 of an hour, John traveled 15 × 2/3 = 10 miles (rt = d)
In that same 2/3 of an hour, Jacob traveled 12 × 2/3 = 8 miles
John therefore had a two-mile lead when he stopped to fix his tire.
In 2/3 of an hour, John traveled 15 × 2/3 = 10 miles (rt = d)
In that same 2/3 of an hour, Jacob traveled 12 × 2/3 = 8 miles
John therefore had a two-mile lead when he stopped to fix his tire.
It took John 1 hour to fix his tire, during which time Jacob traveled 12 miles. Since John began this 1-hour period 2 miles ahead, at the end of the period he is 12 – 2 = 10 miles behind Jacob.
The question now becomes "how long does it take John to bridge the 10-mile gap between him and Jacob, plus whatever additional distance Jacob has covered, while traveling at 15 miles per hour while Jacob is traveling at 12 miles per hour?" We can set up an rt = d chart to solve this.
The question now becomes "how long does it take John to bridge the 10-mile gap between him and Jacob, plus whatever additional distance Jacob has covered, while traveling at 15 miles per hour while Jacob is traveling at 12 miles per hour?" We can set up an rt = d chart to solve this.
John's travel during this "catch-up period" can be represented as 15t = d + 10
Jacob's travel during this "catch-up period" can be represented as 12t = d
Jacob's travel during this "catch-up period" can be represented as 12t = d
If we solve these two simultaneous equations, we get:
15t = 12t + 10
3t = 10
t = 3 1/3 hours
Another way to approach this question is to note that when John begins to ride again, Jacob is 10 miles ahead. So John must make up those first 10 miles plus whatever additional distance Jacob has covered while both are riding. Since Jacob's additional distance at any given moment is 12t (measuring from the moment when John begins riding again) we can represent the distance that John has to make up as 12t + 10. We can also represent John's distance at any given moment as 15t. Therefore, 15t = 12t + 10, when John catches up to Jacob. We can solve this question as outlined above.
15t = 12t + 10
3t = 10
t = 3 1/3 hours
Another way to approach this question is to note that when John begins to ride again, Jacob is 10 miles ahead. So John must make up those first 10 miles plus whatever additional distance Jacob has covered while both are riding. Since Jacob's additional distance at any given moment is 12t (measuring from the moment when John begins riding again) we can represent the distance that John has to make up as 12t + 10. We can also represent John's distance at any given moment as 15t. Therefore, 15t = 12t + 10, when John catches up to Jacob. We can solve this question as outlined above.
The correct answer is B.
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John and Jacob set out together on bicycle traveling at 15 and 12 miles per hour, respectively. After 40minutes, John stops to fix a flat tire. If it takes John one hour to fix the flat tire and Jacob continues to ride during this time, how many hours will it take John to catch up to Jacob assuming he resumes his ride at 15 miles per hour? (consider John's deceleration/acceleration before/after the flat to be negligible)a)3b)3.33c)d)4e)Correct answer is option 'B'. Can you explain this answer?
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John and Jacob set out together on bicycle traveling at 15 and 12 miles per hour, respectively. After 40minutes, John stops to fix a flat tire. If it takes John one hour to fix the flat tire and Jacob continues to ride during this time, how many hours will it take John to catch up to Jacob assuming he resumes his ride at 15 miles per hour? (consider John's deceleration/acceleration before/after the flat to be negligible)a)3b)3.33c)d)4e)Correct answer is option 'B'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about John and Jacob set out together on bicycle traveling at 15 and 12 miles per hour, respectively. After 40minutes, John stops to fix a flat tire. If it takes John one hour to fix the flat tire and Jacob continues to ride during this time, how many hours will it take John to catch up to Jacob assuming he resumes his ride at 15 miles per hour? (consider John's deceleration/acceleration before/after the flat to be negligible)a)3b)3.33c)d)4e)Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for John and Jacob set out together on bicycle traveling at 15 and 12 miles per hour, respectively. After 40minutes, John stops to fix a flat tire. If it takes John one hour to fix the flat tire and Jacob continues to ride during this time, how many hours will it take John to catch up to Jacob assuming he resumes his ride at 15 miles per hour? (consider John's deceleration/acceleration before/after the flat to be negligible)a)3b)3.33c)d)4e)Correct answer is option 'B'. Can you explain this answer?.
John and Jacob set out together on bicycle traveling at 15 and 12 miles per hour, respectively. After 40minutes, John stops to fix a flat tire. If it takes John one hour to fix the flat tire and Jacob continues to ride during this time, how many hours will it take John to catch up to Jacob assuming he resumes his ride at 15 miles per hour? (consider John's deceleration/acceleration before/after the flat to be negligible)a)3b)3.33c)d)4e)Correct answer is option 'B'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about John and Jacob set out together on bicycle traveling at 15 and 12 miles per hour, respectively. After 40minutes, John stops to fix a flat tire. If it takes John one hour to fix the flat tire and Jacob continues to ride during this time, how many hours will it take John to catch up to Jacob assuming he resumes his ride at 15 miles per hour? (consider John's deceleration/acceleration before/after the flat to be negligible)a)3b)3.33c)d)4e)Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for John and Jacob set out together on bicycle traveling at 15 and 12 miles per hour, respectively. After 40minutes, John stops to fix a flat tire. If it takes John one hour to fix the flat tire and Jacob continues to ride during this time, how many hours will it take John to catch up to Jacob assuming he resumes his ride at 15 miles per hour? (consider John's deceleration/acceleration before/after the flat to be negligible)a)3b)3.33c)d)4e)Correct answer is option 'B'. Can you explain this answer?.
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