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Answer :
- To find the distance traveled in $3 \frac{1}{2}$ hours, multiply the speed (90 km/hour) by the time (3.5 hours): $d = 90 \times 3.5 = 315$ km.
- To find the time it takes to travel 390 km, divide the distance (390 km) by the speed (90 km/hour): $t = \frac{390}{90} = \frac{13}{3}$ hours.
- Convert $\frac{13}{3}$ hours to $4 \frac{1}{3}$ hours, which is 4 hours and 20 minutes.
- The car travels 315 km in $3 \frac{1}{2}$ hours, and it takes $4 \frac{1}{3}$ hours to travel 390 km. The answers are: $\boxed{315 \text{ km}}$ and $\boxed{4 \frac{1}{3} \text{ hours}}$.
### Explanation
1. Problem Analysis
Let's analyze the problem. We are given the average speed of a car and asked to find the distance it travels in a given time and the time it takes to travel a given distance.
2. Finding the Distance
For question 4.3.1, we need to find the distance the car travels in $3 \frac{1}{2}$ hours at an average speed of 90 km/hour. We know that distance = speed $\times$ time. So, we have:
$$d = v \times t$$
where $d$ is the distance, $v$ is the speed, and $t$ is the time.
3. Calculating the Distance
We are given $v = 90$ km/hour and $t = 3 \frac{1}{2} = 3.5$ hours. Plugging these values into the formula, we get:
$$d = 90 \times 3.5 = 315$$
So, the car will travel 315 km in $3 \frac{1}{2}$ hours.
4. Finding the Time
For question 4.3.2, we need to find the time it takes for the car to travel 390 km at the same speed of 90 km/hour. We know that time = distance / speed. So, we have:
$$t = \frac{d}{v}$$
5. Calculating the Time
We are given $d = 390$ km and $v = 90$ km/hour. Plugging these values into the formula, we get:
$$t = \frac{390}{90} = \frac{39}{9} = \frac{13}{3} = 4 \frac{1}{3}$$
So, it will take the car $4 \frac{1}{3}$ hours to travel 390 km.
6. Converting to Hours and Minutes
Since $\frac{1}{3}$ of an hour is 20 minutes, the time is 4 hours and 20 minutes.
7. Final Answer
Therefore, the car will travel 315 km in $3 \frac{1}{2}$ hours, and it will take the car $4 \frac{1}{3}$ hours (or 4 hours and 20 minutes) to travel 390 km.
### Examples
Understanding the relationship between speed, distance, and time is crucial in everyday life. For instance, when planning a road trip, you can use these calculations to estimate how long it will take to reach your destination based on your average speed. Similarly, delivery services rely on these calculations to optimize routes and provide accurate delivery time estimates. This concept is also fundamental in fields like aviation and logistics, where precise timing and distance calculations are essential for safe and efficient operations.
- To find the time it takes to travel 390 km, divide the distance (390 km) by the speed (90 km/hour): $t = \frac{390}{90} = \frac{13}{3}$ hours.
- Convert $\frac{13}{3}$ hours to $4 \frac{1}{3}$ hours, which is 4 hours and 20 minutes.
- The car travels 315 km in $3 \frac{1}{2}$ hours, and it takes $4 \frac{1}{3}$ hours to travel 390 km. The answers are: $\boxed{315 \text{ km}}$ and $\boxed{4 \frac{1}{3} \text{ hours}}$.
### Explanation
1. Problem Analysis
Let's analyze the problem. We are given the average speed of a car and asked to find the distance it travels in a given time and the time it takes to travel a given distance.
2. Finding the Distance
For question 4.3.1, we need to find the distance the car travels in $3 \frac{1}{2}$ hours at an average speed of 90 km/hour. We know that distance = speed $\times$ time. So, we have:
$$d = v \times t$$
where $d$ is the distance, $v$ is the speed, and $t$ is the time.
3. Calculating the Distance
We are given $v = 90$ km/hour and $t = 3 \frac{1}{2} = 3.5$ hours. Plugging these values into the formula, we get:
$$d = 90 \times 3.5 = 315$$
So, the car will travel 315 km in $3 \frac{1}{2}$ hours.
4. Finding the Time
For question 4.3.2, we need to find the time it takes for the car to travel 390 km at the same speed of 90 km/hour. We know that time = distance / speed. So, we have:
$$t = \frac{d}{v}$$
5. Calculating the Time
We are given $d = 390$ km and $v = 90$ km/hour. Plugging these values into the formula, we get:
$$t = \frac{390}{90} = \frac{39}{9} = \frac{13}{3} = 4 \frac{1}{3}$$
So, it will take the car $4 \frac{1}{3}$ hours to travel 390 km.
6. Converting to Hours and Minutes
Since $\frac{1}{3}$ of an hour is 20 minutes, the time is 4 hours and 20 minutes.
7. Final Answer
Therefore, the car will travel 315 km in $3 \frac{1}{2}$ hours, and it will take the car $4 \frac{1}{3}$ hours (or 4 hours and 20 minutes) to travel 390 km.
### Examples
Understanding the relationship between speed, distance, and time is crucial in everyday life. For instance, when planning a road trip, you can use these calculations to estimate how long it will take to reach your destination based on your average speed. Similarly, delivery services rely on these calculations to optimize routes and provide accurate delivery time estimates. This concept is also fundamental in fields like aviation and logistics, where precise timing and distance calculations are essential for safe and efficient operations.
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