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George and Bill left town A for town B at the same time.

George and Bill left town A for town B at the same time. George was riding a bicycle at a constant speed, while Bill was driving a car. Bill traveled 5 times faster than George. Bill's car broke halfway, and the rest of the way to the town B Bill traveled by foot with a speed equal to half of the George's bicycle speed. Who got to B first: George or Bill?

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Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...
4.8 4.8 (4 lesson ratings) (4)
 George Speed -  X
 Bills Speed      - 5X
 Bills speed by foot - X/2
  d- distance from A-B
     X  = d/t1           5X + X/2 =d/t2
                             11X/2 = d/ t2
   t1= d/X ---------------- time it takes Bill to go from A to B
    t2 = d/ (11X/2)---------- Time it will take George to go from A to B
     t1= d/X
       t1 > t2 ,   Therefore Bill reaches earlier.
       Note : The formula used was  
       Speed * ( time it would take) = distance traveled.
Kirill Z. | Physics, math tutor with great knowledge and teaching skillsPhysics, math tutor with great knowledge...
4.9 4.9 (174 lesson ratings) (174)
Let D be the distance between A and B. Let also George's speed be V. Then Bill's car speed was 5V, his walking speed was V/2.
Time it took George to get to B:
time it took Bill to get to B:
It is immediately obvious that, since George's time is L/V, it took Bill longer to get to B. In fact, it took him 11/10*(L/V)=11/10*tG, where tG is the time it took George to get from A to B.
So George got to B first.
Mark P. | Experienced math and physics tutorExperienced math and physics tutor
4.7 4.7 (45 lesson ratings) (45)
The time George completed the trip:  t = AB/v
The time Bill completed the trip: t(total) = t1 + t2
The time for the first half of the trip (car is not broken):  t1 = (AB/2) / 5v = AB/10v
The time for the second half (by foot):  t2 = (AB/2) / (v/2) = AB/v
Total time for Bill : T = t1 + t2 = AB/10v + AB/v. This time is longer than George's time ( AB/v)
Answer: George got to B first