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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To find the distance the car travels at an average speed of \( 100 \mathrm{~km/h} \) for \( 3 \) hours and \( 20 \) minutes, we first convert the time to hours. \( 3 \) hours and \( 20 \) minutes is \( 3 + \frac{20}{60} = 3.3333 \) hours. Now, we calculate the distance: \[ \text{Distance} = \text{Speed} \times \text{Time} = 100 \mathrm{~km/h} \times 3.3333 \,\text{h} = 333.33 \mathrm{~km} \] Next, to cover the same distance in \( 2 \) hours and \( 40 \) minutes, we convert the time to hours as well: \( 2 \) hours and \( 40 \) minutes equals \( 2 + \frac{40}{60} = 2.6667 \) hours. To find the constant speed required: \[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{333.33 \mathrm{~km}}{2.6667 \,\text{h}} \approx 125 \mathrm{~km/h} \] Therefore, the car must travel at a constant speed of approximately \( 125 \mathrm{~km/h} \) to cover the same distance in \( 2 \) hours and \( 40 \) minutes.