In a 1000 m race, X beats Y by 140 m or 14 s. What is X's time over the full course?

Introduction / Context:A dual margin (distance or time) lets us determine the slower runner's speed and then deduce the winner's finishing time using the provided time gap.

Given Data / Assumptions:

• Race length = 1000 m.
• X beats Y by 140 m or 14 s (these are equivalent).
• Speeds are constant during the race.

Concept / Approach:If 140 m corresponds to 14 s for Y, then Y's speed is determined. Y's 1000 m time minus the 14 s gap gives X's course time.

Step-by-Step Solution: Y's speed = 140 m / 14 s = 10 m/s Y's 1000 m time = 1000 / 10 = 100 s X's time = 100 − 14 = 86 s

Verification / Alternative check:In 86 s at 10 m/s, Y would cover 860 m; indeed, X finishes the full 1000 m, leading by 140 m, aligning with the data.

Why Other Options Are Wrong:90 s or 95 s would not produce a 140 m lead at Y's 10 m/s; 76 s would exaggerate the margin beyond 140 m.

Common Pitfalls:Assigning the 10 m/s to X instead of Y; forgetting that the 14 s is Y's delay after X finishes.

Final Answer:86 s