In a 1 km race, runner A beats runner B by 28 meters or 7 seconds.
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In a 1 km race, runner A beats runner B by 28 meters or 7 seconds. Find runner A's time over the entire course.
Show answer & explanation
When A finishes 1000 m, B is 28 m behind (at 972 m) and takes 7 more seconds to cover those 28 m. This means B's speed is 28/7 = 4 m/s. Since B takes 7 seconds to cover the remaining distance after A finishes, B's total time is (1000/4) + 7 = 250 + 7 = 257 seconds. A finishes 7 seconds earlier, so A's time is 257 - 7 = 250 seconds. Wait—recalculating: B covers 1000 m at 4 m/s in 250 seconds total. When A finishes 1000 m, B has run 972 m, which takes 972/4 = 243 seconds. So A's time is 243 seconds.
Step-by-step Derivation:
Step 1: Interpret the given information.
- When A finishes 1 km (1000 m), B is 28 m behind (at 972 m).
- B takes 7 more seconds to cover those remaining 28 m.
Step 2: Find B's speed.
- B covers 28 m in 7 seconds.
- B's speed = 28/7 = 4 m/s.
Step 3: Find the time when A finishes.
- When A finishes 1000 m, B has covered 972 m.
- Time for B to cover 972 m at 4 m/s = 972/4 = 243 seconds.
- Since A and B run simultaneously, A also finishes in 243 seconds.
Step 4: Verify.
- A's speed = 1000/243 ≈ 4.115 m/s.
- After 243 seconds, B covers 4 × 243 = 972 m.
- B is 1000 - 972 = 28 m behind. ✓
- B needs 28/4 = 7 more seconds to finish. ✓
Answer: A's time = 243 seconds.