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.
Car Overtake Time Ec1173
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