Race and Rest
Algebra
Level
3
Allan, Bryan, and Charles are going to race in a 100 km track.
- Allan can move 30 km in 60 minutes and need to stop for 30 minutes to regain stamina.
- Bryan can move 20 km in 40 minutes and need to stop for 20 minutes to regain stamina.
- Charles can move 10 km in 20 minutes and need to stop for 10 minutes to regain stamina.
When they reached 100 km they don't need to regain stamina anymore.
Which of the statements is correct?
- A. Allan is the fastest.
- B. Bryan is the slowest.
- C. Charles finish the race in 290 minutes.
- D. Allan and Charles finish the race in same time.
- E. Bryan finish the race in 280 minutes.
C D E
A D E
A B C
A C E
B C D
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1 solution
Allan can move 30 km in 60 minutes and rest for 30 minutes, we can say his speed is 30 km / 90 minutes. He takes 270 minutes to move 90 km. To reach 10 km he needs another 20 minutes, therefore Allan finish the race in 290 minutes.
Bryan speed is 20 km in 40 minutes and 20 minutes rest, we can say his speed is 20 km / 60 minutes. He take 240 minutes to move 80 km. To reach 20 km he needs another 40 minutes, making total time of 280 minutes.
Charlie has the same speed as Allan, they both finish the race in same time.
The correct answer is C D E.