13. A car travelling at an average speed of $$ 100 \mathrm{~km} / \mathrm{h} $$ covers a certain distance in 3 hours 20 minutes. At what constant speed must the car travel to cover the same distance in 2 hours and 40 minutes?

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1. Convert the times to hours:
   - $$3$$ hours $$20$$ minutes is  
     $$
     3 + \frac{20}{60} = 3 + \frac{1}{3} = \frac{10}{3} \text{ hours.}
     $$
   - $$2$$ hours $$40$$ minutes is  
     $$
     2 + \frac{40}{60} = 2 + \frac{2}{3} = \frac{8}{3} \text{ hours.}
     $$

2. Calculate the distance using the original speed:
   - The distance $$D$$ is given by the formula  
     $$
     D = \text{speed} \times \text{time} = 100 \times \frac{10}{3} = \frac{1000}{3} \text{ km.}
     $$

3. Determine the required speed to cover the same distance in $$\frac{8}{3}$$ hours:
   - Let the new constant speed be $$v$$. Then,  
     $$
     v = \frac{D}{\text{time}} = \frac{\frac{1000}{3}}{\frac{8}{3}} = \frac{1000}{8} = 125 \text{ km/h.}
     $$

Thus, the car must travel at a constant speed of $$125 \text{ km/h}$$ to cover the distance in $$2$$ hours $$40$$ minutes.
The car needs to travel at $$125 \text{ km/h}$$ to cover the same distance in $$2$$ hours $$40$$ minutes.

13. A car travelling at an average speed of \( 100 \mathrm{~km} / \mathrm{h} \) covers a certain distance in 3 hours 20 minutes. At what constant speed must the car travel to cover the same distance in 2 hours and 40 minutes?

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