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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

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by BTGmoderatorDC » Wed Oct 19, 2022 5:40 am

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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)

A. 3
B. 3 1/3
C. 3 1/2
D. 4
E. 4 1/2


OA B

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Re: John and Jacob set out together on bicycle traveling at 15 and 12 miles per hour, respectively. After 40 minutes, Jo

by Scott@TargetTestPrep » Tue Dec 06, 2022 7:47 pm
BTGmoderatorDC wrote: ↑
Wed Oct 19, 2022 5:40 am
 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)

A. 3
B. 3 1/3
C. 3 1/2
D. 4
E. 4 1/2


OA B

Source: Manhattan Prep
In the first 40 minutes John is 2/3(15 - 12) = 2/3 x 3 = 2 miles ahead of Jacob.

While John is fixing the flat, Jacob travels 12 miles.

So, when John starts back up, Jacob is now 12 - 2 = 10 miles ahead of John.

Since the difference between John and Jacob's rates is 15 - 12 = 3, and since Jacob is 10 miles ahead of John, he needs 10/3 = 3 1/3 hours to catch Jacob.

Answer: B

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