AMC 10 Weekly Practice Round 2
Complete problem set with solutions and individual problem pages
The distance between and is km. Two people, and , set out at the same time from to on bicycles. Person rides km per day, while person rides km per day but rests every other day. At the end of the day, the distance from for person is twice the distance from for person .
- A.
- B.
- C.
- D.
- E.
Casework:
(1) If the number of days is even, then for it is equivalent to riding $$
50 \text{km per day}.$$
Let be the number of days such that at the end of day , B’s distance from is twice ’s distance from .
We have the equation: which gives not a valid solution.
(2) If the number of days is odd, then except for the last day (when rides km), rides km per day on the previous days.
Let be the number of days such that at the end of day , ’s distance from is twice ’s distance from .
We have the equation which gives a valid solution.
Thus, at the end of the 15th day, ’s distance from is twice ’s distance from .
