John and Jacob set out together on bicycle traveling at 15 and 12 miles per hour, respectively.
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 two 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)
Answer/Solution
7 1/3
Steps/Work
John's speed - 15 miles/hr
Jacob's speed - 12 miles/hr
After 40min (i.e 2/3hr), distance covered by John = 15x2/3 = 10 miles.
Jacob continues to ride for a total of 2 hour and 40min (until John's bike is repaired). Distance covered in 2 hour 40min (i.e 8/3hr) = 12x8/3 = 32 miles.
Now, when John starts riding back, the distance between them is 22 miles. Jacob and John are moving in the same direction.For John to catch Jacob, the effective relative speed will be 15-12 = 3 miles/hr.
Thus, to cover 22 miles at 3 miles/hr, John will take 22/3 = 7 1/3 hours
Answer B
Jacob's speed - 12 miles/hr
After 40min (i.e 2/3hr), distance covered by John = 15x2/3 = 10 miles.
Jacob continues to ride for a total of 2 hour and 40min (until John's bike is repaired). Distance covered in 2 hour 40min (i.e 8/3hr) = 12x8/3 = 32 miles.
Now, when John starts riding back, the distance between them is 22 miles. Jacob and John are moving in the same direction.For John to catch Jacob, the effective relative speed will be 15-12 = 3 miles/hr.
Thus, to cover 22 miles at 3 miles/hr, John will take 22/3 = 7 1/3 hours
Answer B