To determine how long it will take for the car traveling at 65 mph to pass the car traveling at 50 mph, we need to consider the initial lead and the speed difference between the two cars.
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Initial lead: The solar car has a 2-hour lead.
- In 2 hours, the car traveling at 50 mph covers: \[ \text{Distance} = \text{Speed} \times \text{Time} = 50 , \text{mph} \times 2 , \text{hours} = 100 , \text{miles}. \] So, the car traveling at 50 mph is initially 100 miles ahead.
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Speed difference: The speed difference between the two cars is: \[ \text{Speed difference} = 65 , \text{mph} - 50 , \text{mph} = 15 , \text{mph}. \]
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Time to catch up: To find the time it takes for the faster car (65 mph) to catch the slower car (50 mph), we use the formula \[ \text{Time} = \frac{\text{Distance}}{\text{Speed difference}}. \] Plugging in the values: \[ \text{Time} = \frac{100 , \text{miles}}{15 , \text{mph}} \approx 6.67 , \text{hours}. \]
Therefore, it will take approximately 6.67 hours (or about 6 hours and 40 minutes) for the car traveling at 65 mph to pass the car traveling at 50 mph.