1.14 使用距离公式寻找距离、速度和时间

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  使用距离公式查找距离、速度和时间

  

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  Kevin and his family are going camping in Yellowstone National Park. Kevin tracked the family’s journey from Denver on his map and saw that they drove about 540 miles in nine hours. The family only made brief stops along the way, and Kevin wants to know how fast the car must have been traveling. How can Kevin calculate the car’s speed based on the information he already has?
  ::Kevin和他的家人正在黄石公园露营。 Kevin在他的地图上追踪了家人从丹佛的行程,看到他们九小时开540英里。 家人在路上只停留了短暂的路程,Kevin想知道汽车的行驶速度。 Kevin如何根据他已经掌握的信息计算汽车的速度?

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  In this concept, you will learn to use the formula for distance to calculate distances, rates and times.
  ::在此概念中,您将学会使用距离公式来计算距离、速度和时间。

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  Distance, Rate and Time
  ::距离、速度和时间

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  Formulas can be used to calculate distance, rate and time.
  ::公式可用于计算距离、速度和时间。

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  Distance is the measure of how far you travel. The rate is the measure of the speed that you travel. How long you travel is the measure of time .
  ::距离是测量您行走多远的尺度。 速度是测量您行走速度的尺度。 旅行多长时间是测量时间的尺度 。

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  When using the formula involving distance, rate, and time, it is essential that you pay attention to the units used in the problem. If the rate in the problem gives miles per hour (mph), then time must be in hours. If the time is given in minutes, divide by sixty to determine the number of hours prior to solving the equation .
  ::当使用涉及距离、速率和时间的公式时,您必须注意问题中使用的单位。如果问题的速率给出每小时英里数(mph),那么时间必须是小时数。如果时间以分钟计,则除以60以决定解方程之前的小时数。

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  To find distance, use the formula:
  ::要找到距离, 请使用公式 :

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  $$\begin{array}{r}\text{Distance}=\text{rate}\times \text{time}\end{array}$$

  
  ::距离=时间

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  To find rate, divide both sides of the equation by time.
  ::为了找到比率,将等式的两边按时间分开。

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  $$\begin{array}{r}\text{Rate}=\frac{\text{Distance}}{\text{Time}}\end{array}$$

  
  ::速率=差时

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  To find time, divide both sides of the equation by rate.
  ::寻找时间,将等式的两边除以速率。

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  $$\begin{array}{r}\text{Time}=\frac{\text{Distance}}{\text{Rate}}\end{array}$$

  
  ::时间=差数Rate

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  Let’s look at an example.
  ::让我们举个例子。

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  The Murphy Family drove for three and a half hours from Manhattan, New York to Providence, Rhode Island at a rate of fifty-three miles per hour. Determine the distance the Murphy’s traveled.
  ::墨菲家族从纽约曼哈顿开往罗得岛普罗维登斯的车程为3个半小时,每小时53英里。 确定墨菲的行驶距离。

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  First, you need to think about what you are asked to solve for. In this problem, you need to figure out the distance that the Murphy family traveled.
  ::首先,你需要想一想你被要求解决什么问题。在这个问题上,你需要弄清楚墨菲家族所走的距离。

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  $$\begin{array}{r}\text{Distance}=\text{rate}\times \text{time}\end{array}$$

  
  ::距离=时间

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  Next, take the given information from the problem and substitute that information into the formula.
  ::其次,从问题中取出所提供的信息,并将这些信息替换为公式。

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  $$\begin{array}{r}\begin{array}{rcl}\text{Distance}& =& \text{rate}\times \text{time}\\ \text{Distance}& =& 53mph\times 3.5h\end{array}\end{array}$$

  
  ::远程=ratextime distance=53 mphx3.5 h

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  Then, calculate the distance by multiplying the rate by the time.
  ::然后,通过乘以时速计算距离。

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  $$\begin{array}{r}\begin{array}{rcl}\text{Distance}& =& 53\times 3.5\\ \text{Distance}& =& 185.5\end{array}\end{array}$$

  
  ::距离=53x3.5 距离=185.5

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  The answer is 185.5.
  ::答案是185.5。

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  The distance that the Murphy family traveled was 185.5 miles.
  ::墨菲一家旅行的距离是185.5英里

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  Examples 
  ::实例

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  Example 1
  ::例1

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  Earlier, you were given a problem about  Kevin’s family vacation.
  ::Kevin的家事假期问题。

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  Kevin knows that they drove 540 miles in nine hours and wants to determine how fast they were driving, that is, the rate.
  ::凯文知道他们九小时内开540英里 想要确定他们开的有多快 也就是速率

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  First, consider the formula to solve for the rate.
  ::首先,考虑解决费率的公式。

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  $$\begin{array}{r}\text{Rate}=\frac{\text{Distance}}{\text{Time}}\end{array}$$

  
  ::速率=差时

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  Next, fill in what you know.
  ::接下来 填上你所知道的

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  $$\begin{array}{r}x=\frac{540}{9}\end{array}$$

  
  ::x=5409

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  Then, solve for $\begin{array}{r}x\end{array}$ .
  ::那么,解决x。

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  $$\begin{array}{r}\begin{array}{rcl}x& =& \frac{540}{9}\\ x& =& 60\end{array}\end{array}$$

  
  ::x=5409x=60

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  The answer is 60.
  ::答案是60岁

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  The rate (speed) is 60 mph.
  ::速度(速度)为60米。

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  Example 2
  ::例2

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  A train traveled 255 miles in 300 minutes. Determine the rate at which the train was traveling.
  ::火车在300分钟内行驶255英里 确定火车的行驶速度

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  First, convert the 300 minutes into hours since rate (or speed) is normally measured in miles per hour.
  ::首先,将300分钟转换成小时,因为标准(或速度)通常以每小时英里计量。

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  $$\begin{array}{r}\begin{array}{rcl}\mathrm{\#}hours& =& 300min\times \frac{1hour}{60min}\\ \mathrm{\#}hours& =& 5hr\end{array}\end{array}$$

  
  ::# 小时= 300 分钟1x1小时60 分钟# 小时= 5小时

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  Next, use the rate formula to find the rate.
  ::接下来,使用速率公式来找到速率。

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  $$\begin{array}{r}\begin{array}{rcl}\text{Rate}& =& \frac{\text{Distance}}{\text{Time}}\\ \text{Rate}& =& \frac{255}{5}\\ \text{Rate}& =& 51\end{array}\end{array}$$

  
  ::速率=残疾时间Rate=2555Rate=51

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  The answer is 50.
  ::答案是50

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  The train was travelling at a rate (or speed) of 51 miles per hour.
  ::火车的车速(或速度)为每小时51英里。

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  Example 3
  ::例3

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  Use the to solve for rate.
  ::使用以解答利率 。

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  $\begin{array}{r}\text{Distance}=285miles\end{array}$
  ::距离=285英里

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  $\begin{array}{r}\text{Time}=9.5hours\end{array}$
  ::时间=9.5小时

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  $\begin{array}{r}\text{Rate}=x\end{array}$
  ::费率=x

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  First, write down the formula to solve for the rate.
  ::首先,写下解答利率的公式。

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  $$\begin{array}{r}\text{Rate}=\frac{\text{Distance}}{\text{Time}}\end{array}$$

  
  ::速率=差时

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  Next, fill in what you know.
  ::接下来 填上你所知道的

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  $$\begin{array}{r}x=\frac{285}{9.5}\end{array}$$

  
  ::x=2859.5

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  Then, solve for $\begin{array}{r}x\end{array}$ .
  ::那么,解决x。

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  $$\begin{array}{r}\begin{array}{rcl}x& =& \frac{285}{9.5}\\ x& =& 30\end{array}\end{array}$$

  
  ::x=2859.5x=30

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  The answer is 30.
  ::答案是30岁

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  The rate (speed) is 30 mph.
  ::速度(速度)为30米。

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  Example 4
  ::例4

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  Use the distance formula to solve for time.
  ::使用距离公式解析时间 。

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  $\begin{array}{r}\text{Distance}=550miles\end{array}$
  ::距离=550英里

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  $\begin{array}{r}\text{Rate}=55mph\end{array}$  
  ::速率=55毫米/小时

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  $\begin{array}{r}\text{Time}=x\end{array}$
  ::时间=x

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  First, write down the formula to solve for the time.
  ::首先, 写下要解析的公式 。

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  $$\begin{array}{r}\text{Time}=\frac{\text{Distance}}{\text{Rate}}\end{array}$$

  
  ::时间=差数Rate

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  Next, fill in what you know.
  ::接下来 填上你所知道的

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  $$\begin{array}{r}x=\frac{550}{55}\end{array}$$

  
  ::x=55055

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  Then, solve for $\begin{array}{r}x\end{array}$ .
  ::那么,解决x。

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  $$\begin{array}{r}\begin{array}{rcl}x& =& \frac{550}{55}\\ x& =& 10\end{array}\end{array}$$

  
  ::x=55055x=10

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  The answer is 10.
  ::答案是10个

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  The time is 10 hours.
  ::时间是10小时

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  Example 5
  ::例5

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  A car traveled 45 mph for 6 hours. How many miles did it travel?
  ::一辆45英里长的车行驶了6小时 飞行了几英里?

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  First, write down the formula to solve for the distance.
  ::首先,写下解析距离的公式。

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  $$\begin{array}{r}\text{Distance}=\text{Rate}\times \text{Time}\end{array}$$

  
  ::距离=时间

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  Next, fill in what you know.
  ::接下来 填上你所知道的

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  $$\begin{array}{r}x=45\times 6\end{array}$$

  
  ::x=45x6

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  Then, solve for $\begin{array}{r}x\end{array}$ .
  ::那么,解决x。

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  $$\begin{array}{r}\begin{array}{rcl}x& =& 45\times 6\\ x& =& 270\end{array}\end{array}$$

  
  ::x=45x6x=270 x=45x6x=270

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  The answer is 270.
  ::答案是270

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  The distance traveled was 270 miles.
  ::距离是270英里

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  Review
  ::回顾

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  Find the number of miles traveled given the rate and time.
  ::找到根据速率和时间所经过的英里数 。

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  1. 4 hours at a rate of 33 mph.
  ::1. 4小时,按33米的速率计算。

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  2. 6 hours at a rate of 55 mph.
  ::2. 6小时,每小时55米。

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  3. 8 hours at a rate of 65 mph.
  ::3. 8小时,按65英里的速率计算。

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  4. 12 hours at a rate of 50 mph.
  ::4. 12小时,每小时50米。

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  5. 14 hours at a rate of 60 mph.
  ::5. 14小时,每小时60米。

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  6. 19 hours at a rate of 50 mph.
  ::6.19小时,每小时50米。

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  7. 11 hours at a rate of 55 mph.
  ::7. 11小时,每小时55米。

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  8. 18 hours at a rate of 35 mph.
  ::8. 18小时,按每小时35米的速率计算。

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  9. 12 hours at a rate of 70 mph.
  ::9. 12小时,速率为70米。

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  10. 10 hours at a rate of 58 mph.
  ::10小时10小时,每小时58米。

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  11. 15 hours at a rate of 57 mph.
  ::11小时15小时,每小时57英里。

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  12. 21 hours at a rate of 66 mph.
  ::12小时21小时,每小时66米。

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  Use the given information to figure out each rate or time.
  ::使用给定的信息来计算每一速率或时间。

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  13. A car traveled 450 miles at a speed of 30 mph. How many hours did it take?
  ::13. 一辆汽车以30米长的速度行驶450英里,需要多少小时?

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  14. A car traveled 600 miles in 12 hours. What was the speed of the car?
  ::14. 一辆汽车在12小时内行驶了600英里,车速是多少?

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  15. A runner traveled 6 miles in 30 minutes. How fast was the runner going?
  ::15. 一名跑者在30分钟内行驶6英里,跑者跑多快?

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  16. A car traveled 520 miles at a speed of 65 mph. How many hours did it take?
  ::16. 一辆汽车以65英里的速度行驶520英里,需要多少小时?

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  Review (Answers)
  ::回顾(答复)

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  Click to see the answer key or go to the Table of Contents and click on the Answer Key under the 'Other Versions' option.
  ::单击可查看答题键, 或转到目录中, 单击“ 其他版本” 选项下的答题键 。