What is the greatest number of remaining sections the rider can complete without exceeding the 150-minute limit?

Question

A mountain bike race must be finished in no more than 150 minutes. A rider has already spent 42 minutes on the opening climb. Each remaining section of the course takes her 9 minutes to ride.

Accepted Answer

B. 12. If s is the number of remaining sections, then 42 + 9s ≤ 150, so 9s ≤ 108 and s ≤ 12. Since s = 12 gives exactly 150 minutes, which is allowed, the greatest value is 12. Choice A comes from wrongly discarding the boundary value 12 even though 150 minutes is permitted. Choice C ignores the 42 minutes already used and computes 150 ÷ 9 ≈ 16.7. Choice D adds the 42 minutes instead of subtracting it, computing (150 + 42) ÷ 9 ≈ 21.3.

Answer

A. 11 — Since s = 12 gives exactly 150 minutes and the limit allows 150, you shouldn't discard 12 — the inequality is ≤, not <.

Answer

C. 16 — You divided 150 by 9 and ignored the 42 minutes already spent climbing. Subtract first: (150 − 42)/9 = 12.

Answer

D. 21 — You added the 42 minutes instead of subtracting them, computing (150 + 42)/9 ≈ 21.3. The 42 minutes are already used up, so only 108 minutes remain.

Algebra practice question

Answer: B. 12

Why the other answers are wrong

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