Solving a rational travel equation

Proved

WorkbookSource.problem_27265

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Let $x$ be the desired answer, so that Qiang drove a total of $30+x$ miles in the entirety of his voyage and completed the trip within $\frac{15}{30}+\frac{x}{55}$ hours. Therefore, $\frac{x+30}{\frac{x}{55}+\frac{1}{2}}=50\Rightarrow x=\boxed{110}$ .

Source: InternLM Lean-Workbook, record lean_workbook_27265 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_27265  (x : ℝ)
  (h₀ : 0 < x)
  (h₁ : (x + 30) / (x / 55 + 1 / 2) = 50) :
  x = 110  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_27265; Apache-2.0

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