Problem 2 · AMC 8 Stretch
Core
Ratios, Rates & Proportions
Arithmetic & Operations
consider-extreme-casesfind-the-time
A fly and a jogger start 12 km apart. The jogger runs straight toward the fly's starting spot at 4 km per hour. Meanwhile the fly zooms back and forth at 6 km per hour: it flies to the jogger, turns around, flies back, turns around again, and keeps doing this. The fly keeps flying until the jogger reaches the fly's starting spot. How far does the fly travel in total?
Show answer
Answer: 18 km
Show hints
Hint 1 of 4
The fly's back-and-forth path looks scary, but you only need the TOTAL distance it flies. And distance = speed multiplied by time. So the real question is: how long is the fly in the air?
Still stuck? Show hint 2 →
Hint 2 of 4
Stop trying to follow the fly. Watch the jogger instead. The flying stops the exact moment the jogger finishes the 12 km. So all you need is the jogger's travel time.
Still stuck? Show hint 3 →
Hint 3 of 4
How long does the jogger take to go 12 km at 4 km per hour? Divide: 12 divided by 4.
Show solution
Approach: Find the time, not the path
- The trap is adding up all the tiny back-and-forth flights. The clever move is to think about TIME, not the fly's messy path.
- The fly stops flying when the jogger covers the 12 km. At 4 km/hr that takes \(\dfrac{12}{4}=3\) hours.
- The fly was flying that entire 3 hours at 6 km/hr, so it covers \(6\times3=18\) km.
- The fly travels 18 km. (Notice the puzzle has to tell us when the flying stops, or the answer wouldn't be clear — spotting that hidden assumption is part of careful problem solving.)
Mark:
· log in to save