2016 AMC 8
Complete problem set with solutions and individual problem pages
Annie and Bonnie are running laps around a -meter oval track. They started together, but Annie has pulled ahead, because she runs faster than Bonnie. How many laps will Annie have run when she first passes Bonnie?
- A.
- B.
- C.
- D.
- E.
Solution 1
Each lap Bonnie runs, Annie runs another quarter lap, so Bonnie will run four laps before she is overtaken. This means that Annie and Bonnie are equal so that Annie needs to run another lap to overtake Bonnie. That means Annie will have run laps.
Solution 2
Saying that Bonnie runs meters per second, then Annie will run meters per second. It will take Bonnie seconds to run lap and it would take seconds for Annie to do lap. The LCM of and is . In seconds Bonnie will do laps and Annie will do laps. Since Annie did more lap she passed Bonnie. So the answer is laps.
