In a kilometer race, A beats B by 50 meters or 10 seconds. What time does A take to complete the race?
- 200 sec
- 210 sec
- 150 sec
- 190 sec
Explanation
Step 1: Let A's time = t seconds
- So, B’s time = t + 10 seconds
- B runs 950 meters in t seconds (because when A finishes, B is at 950 meters)
- So B’s speed = 950 / t meters per second
Now use B’s speed to find time B takes to run full 1000 meters:
Time = Distance / Speed = 1000 / (950 / t) = (1000t) / 950
We’re also told that B takes 10 seconds more than A:
So,
(1000t / 950) = t + 10
Multiply both sides by 950:
1000t = 950t + 9500
1000t - 950t = 9500
50t = 9500
t = 190 seconds
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