In a handicap race, P gives Q a start of 25 m and this makes the length of the race for Q equal to 175 m. What is the total official length of the race?

Introduction / Context:In handicap or start problems, the slower contestant runs a shorter course. A start of s meters reduces the distance that contestant must cover by s relative to the official race length L.

Given Data / Assumptions:

• Q's course length is 175 m after receiving a start of 25 m.
• Let official race length be L m.

Concept / Approach:By definition, Q runs L - 25 = 175. Solve for L.

Step-by-Step Solution: L - 25 = 175 ⇒ L = 200 m

Verification / Alternative check:Check units and interpretation: a 25 m head start on a 200 m race makes Q's required distance 175 m. Consistent.

Why Other Options Are Wrong:250, 225, 235 m do not satisfy L - 25 = 175.

Common Pitfalls:Adding instead of subtracting the start; confusing a time handicap with a distance handicap.

Final Answer:200 m