Subjects algebra

Car Overtake Time Ec1173

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1. **State the problem:** A car leaves town M at 9:00 am traveling at 60 km/h. Another car leaves the same town at 10:00 am traveling at 80 km/h. We need to find when the second car overtakes the first car. 2. **Define variables and formula:** Let $t$ be the time in hours after 9:00 am when the second car overtakes the first car. Distance traveled by first car in $t$ hours: $$d_1 = 60t$$ Distance traveled by second car in $(t-1)$ hours (since it starts 1 hour later): $$d_2 = 80(t-1)$$ 3. **Set the distances equal to find when the second car catches up:** $$60t = 80(t-1)$$ 4. **Solve the equation:** $$60t = 80t - 80$$ $$60t - 80t = -80$$ $$-20t = -80$$ $$t = \frac{-80}{-20}$$ $$t = 4$$ 5. **Interpret the result:** $t=4$ means 4 hours after 9:00 am, so at 1:00 pm the second car overtakes the first car. **Final answer:** The second car overtakes the first car at 1:00 pm.