1. **State the problem:** Alina walks to a bookstore 1200 m away at 60 m/min. Her friend cycles at 160 m/min and gives her a ride after some walking. The total time to reach the bookstore is 10 minutes. We need to find how long Alina walked before the ride. 2. **Define variables:** Let $t$ be the walking time in minutes. Then, the riding time is $10 - t$ minutes. 3. **Write the distance equation:** Total distance = distance walked + distance ridden. Distance walked = speed $\times$ time = $60t$ meters. Distance ridden = $160(10 - t)$ meters. So, $$60t + 160(10 - t) = 1200$$ 4. **Solve the equation:** $$60t + 1600 - 160t = 1200$$ $$-100t + 1600 = 1200$$ $$-100t = 1200 - 1600$$ $$-100t = -400$$ $$t = \frac{-400}{-100} = 4$$ 5. **Interpretation:** Alina walked for 4 minutes before her friend gave her a ride. **Final answer:** 4 minutes.