Multiply through by \(v(v+20)\):

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• The time for the first part is \(\frac{120}{v}\) hours.
• The time for the second part is \(\frac{180}{v+20}\) hours.
• The total time is \(\frac{120}{v} + \frac{180}{v+20} = 5\).
• \(120(v+20) + 180v = 5v(v+20)\).
• Simplify: \(120v + 2400 + 180v = 5v^2 + 100v\).
• Combine terms: \(300v + 2400 = 5v^2 + 100v\).

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