8.22问题解决计划比例

章节大纲

• 选择节常规

  折叠 展开

  常规

  全部折叠 展开全部

  • 选择活动新闻通告

    

    新闻通告 讨论区
• 选择节问题解决计划比例

  折叠 展开

  问题解决计划比例

  

  [Figure 1]

  播放段落

  Takeru Kobayashi is a competitive eater famous for eating hot dogs among other things. Once, he ate 110 hot dogs in 10 minutes at the New York State Fair. How many hot dogs can Kobayashi eat in 1 minute?
  ::Takeru Kobayashi是一个以吃热狗等闻名的有竞争力的食狗者。 他曾经在纽约州博览会10分钟内吃了110只热狗。 Kobayashi在1分钟内能吃多少热狗?

  播放段落

  In this concept, you will learn the problem solving strategy: use a  proportion .
  ::在这个概念中,你将学会解决问题的战略:使用比例。

  播放段落

  Problem Solving Plan with Proportions
  ::使用比例解决问题计划

  播放段落

  You can solve ratio problems using  proportions . A  proportion  is an  equation  that shows two  equivalent ratios . In  order  to use a proportion, the ratios in the proportion must also compare the same things.
  ::您可以使用比例解决比例问题。比例是一个方程式,显示两种等值比率。为了使用比例,比例中的比例也必须比较相同的情况。

  播放段落

  Let’s look at a problem.
  ::让我们来看看一个问题。

  播放段落

  A car travels 55 miles in two hours. A bus travels 85 kilometers in two hours. Which vehicle traveled a farther  distance ?
  ::一辆车两小时行驶55英里,一辆车两小时行驶85公里,哪辆车走远?

  播放段落

  This problem compares  speed  per hour; however, it is comparing miles to kilometers. The units are not the same and you cannot use a proportion to solve this problem without converting the units first.
  ::这个问题比较了每小时的速度; 但是, 它比较了英里和公里。 单位不同, 您不能使用比例来解决这个问题, 不首先转换单位 。

  播放段落

  Let’s look at another problem.
  ::让我们来看看另一个问题。

  播放段落

  A cheetah can  run  75 miles per hour. If you could run three times as fast as a cheetah, how fast would you be able to run?
  ::猎豹每小时能跑75英里 如果你跑得比猎豹快三倍 你会跑多快?

  播放段落

  The first ratio compares the cheetah’s speed per hour. The second ratio compares a person’s speed per hour. Both ratios can be written as miles per hour. You can use a proportion to solve this problem.
  ::第一个比率比较了豹每小时的速度。 第二个比率比较了一个人每小时的速度。 两个比率可以以每小时英里表示。 您可以使用一定比例来解决这个问题。

  播放段落

  First, write a proportion showing the comparison.
  ::首先,写一个比例显示比较。

  $$\begin{array}{r}\frac{\text{cheetah's speed}}{\text{number of hours}}=\frac{\text{person's speed}}{\text{number of hours}}\end{array}$$

  播放段落

  Next, take the data and fill it into the proportion.
  ::接下来,将数据填入比例。

  $$\begin{array}{r}\frac{75}{1}=\frac{x}{3}\end{array}$$

  播放段落

  The cheetah runs 75 miles per hour.  Per  means “divided by” and “hour” refers to 1 hour. The numerator is 75 and the denominator is 1. The person runs three times as fast, so he or she would go as far in 1 hour as a cheetah would in 3 hours. The denominator is 3. The person’s speed is unknown so it is represented with the  variable   $\begin{array}{r}x\end{array}$ .
  ::猎豹每小时运行75英里。 每一个代表 " 以 " 和 " 小时 " 代表1小时。 分子为75,分母为1。 分子为75, 分母为1。 个人运行速度是猎豹每小时3小时运行的3倍, 他或她每小时运行1小时, 速度会达到猎豹每小时1小时。 分母为3, 速度未知, 与变量 x 代表速度相同 。

  播放段落

  Then, solve the proportion using cross products.
  ::然后用交叉产品解决比例问题。

  $$\begin{array}{r}\begin{array}{rcl}x& =& 75(3)\\ x& =& 225\end{array}\end{array}$$

  播放段落

  If a person ran three times as fast as a cheetah, he or she would run 225 mph.
  ::如果一个人的跑速是猎豹的三倍,他或她的跑速将是猎豹的225英里。

  播放段落

  Examples
  ::实例

  播放段落

  Example 1
  ::例1

  播放段落

  Earlier, you were given a problem about the competitive eater Takeru Kobayashi.
  ::早些时候,你被问及 竞争对手小林竹鲁

  播放段落

  He once ate 110 hot dogs in 10 minutes. To find out how many hot dogs he can eat in 1 minute, write a proportion and solve for  $\begin{array}{r}x\end{array}$ .
  ::他10分钟内就吃了110只热狗,

  播放段落

  First, set up the proportion.
  ::首先,设定比例。

  $$\begin{array}{r}\frac{\text{hot dogs}}{\text{minutes}}=\frac{\text{hot dogs}}{\text{minutes}}\end{array}$$

  播放段落

  Next, fill in the given information.
  ::下一步填入给定信息。

  $$\begin{array}{r}\frac{110}{10}=\frac{x}{1}\end{array}$$

  播放段落

  Then, cross multiply and solve for  $\begin{array}{r}x\end{array}$ .
  ::然后,交叉乘数并解答 x。

  $$\begin{array}{r}\begin{array}{rcl}10x& =& 110(1)\\ 10x& =& 110\\ x& =& 11\end{array}\end{array}$$

  播放段落

  Takeru Kobayashi can eat 11 hot dogs in 1 minute.
  ::竹鲁小林能在一分钟内吃11只热狗

  播放段落

  Example 2
  ::例2

  播放段落

  Use a proportion to solve the following problem.
  ::使用比例来解决以下问题 。

  播放段落

  If a person can run 3 miles in 20 minutes, how long will it take the same person to run 12 miles at the same  rate ?
  ::如果一个人能在20分钟内跑3英里 同一人要多久才能以同样的速度跑12英里?

  播放段落

  First, set up the proportion.
  ::首先,设定比例。

  $$\begin{array}{r}\frac{\text{miles}}{\text{minutes}}=\frac{\text{miles}}{\text{minutes}}\end{array}$$

  播放段落

  Next, fill in the given information.
  ::下一步填入给定信息。

  $$\begin{array}{r}\frac{3}{20}=\frac{12}{x}\end{array}$$

  播放段落

  Now we cross multiply and solve for  $\begin{array}{r}x\end{array}$ .
  ::现在我们交叉乘数,解决 x。

  $$\begin{array}{r}\begin{array}{rcl}3x& =& 20(12)\\ 3x& =& 240\\ x& =& 80\end{array}\end{array}$$

  播放段落

  The person would run 12 miles in 80 minutes or 1 hour and 20 minutes.
  ::80分钟或1小时20分钟内跑12英里

  播放段落

  Use the following information to answer the next three questions:
  ::使用以下信息回答以下三个问题:

  播放段落

  A cheetah runs 75 miles per hour.
  ::一只猎豹每小时跑75英里

  播放段落

  Example 3
  ::例3

  播放段落

  If you could run twice as fast as a cheetah, how fast could you run?
  ::如果你能跑得比猎豹快两倍 你能跑多快?

  播放段落

  First, set up the proportion.
  ::首先,设定比例。

  $$\begin{array}{r}\frac{\text{miles}}{\text{hour}}=\frac{\text{miles}}{\text{hour}}\end{array}$$

  播放段落

  Next, fill in the given information.
  ::下一步填入给定信息。

  $$\begin{array}{r}\frac{75}{1}=\frac{x}{2}\end{array}$$

  播放段落

  Then, cross multiply and solve for  $\begin{array}{r}x\end{array}$ .
  ::然后,交叉乘数并解答 x。

  $$\begin{array}{r}\begin{array}{rcl}x& =& 75(2)\\ x& =& 150\end{array}\end{array}$$

  播放段落

  You could run 150 miles per hour.
  ::你每小时可以跑150英里

  播放段落

  Example 4
  ::例4

  播放段落

  If you could run half as fast as a cheetah, how fast could you run?
  ::如果你跑得比猎豹快一半 你能跑多快?

  播放段落

  First, set up the proportion.
  ::首先,设定比例。

  $$\begin{array}{r}\frac{\text{miles}}{\text{hour}}=\frac{\text{miles}}{\text{hour}}\end{array}$$

  播放段落

  Next, fill in the given information.
  ::下一步填入给定信息。

  $$\begin{array}{r}\frac{75}{1}=\frac{x}{0.5}\end{array}$$

  播放段落

  Then, cross multiply and solve for  $\begin{array}{r}x\end{array}$ .
  ::然后,交叉乘数并解答 x。

  $$\begin{array}{r}\begin{array}{rcl}x& =& 75(0.5)\\ x& =& 37.5\end{array}\end{array}$$

  播放段落

  You could run 37.5 miles per hour.
  ::你可以跑37.5英里每小时。

  播放段落

  Example 5
  ::例5

  播放段落

  If you could run four times as fast as a cheetah, how fast could you run?
  ::如果你跑得比猎豹快四倍 你能跑多快?

  播放段落

  First, set up the proportion.
  ::首先,设定比例。

  $$\begin{array}{r}\frac{\text{miles}}{\text{hour}}=\frac{\text{miles}}{\text{hour}}\end{array}$$

  播放段落

  Next, fill in the given information.
  ::下一步填入给定信息。

  $$\begin{array}{r}\frac{75}{1}=\frac{x}{4}\end{array}$$

  播放段落

  Then, cross multiply and solve for  $\begin{array}{r}x\end{array}$ .
  ::然后,交叉乘数并解答 x。

  $$\begin{array}{r}\begin{array}{rcl}x& =& 75(4)\\ x& =& 300\end{array}\end{array}$$

  播放段落

  You could run 300 miles per hour.
  
  ::你每小时可以跑300英里

  播放段落

  Review
  ::回顾

  播放段落

  Solve each word problem by using a proportion.
  ::使用比例来解决每个字的问题。

  播放段落
  1. In a diagram for the new garden, one inch is equal to 3 feet. If this is the case, how many feet is the actual garden edge if the measurement on the diagram is 5 inches?
     ::在新花园的图表中,一英寸等于3英尺。如果是这样,如果图上的测量值是5英寸,实际的花园边缘是多少英尺?
  播放段落
  2. If two inches on a map are equal to three miles, how many miles are represented by four inches?
     ::如果地图上两英寸等于三英里, 多少英里代表四英寸?
  播放段落
  3. If eight inches on a map are equal to ten miles, how many miles are 16 inches equal to?
     ::如果地图上8英寸等于10英里 16英寸等于多少英里?
  播放段落
  4. Casey drew a design for bedroom. On the picture, she used one inch to represent five feet. If her bedroom wall is ten feet long, how many inches will Casey draw on her diagram to represent this measurement?
     ::Casey画了一个卧室设计图。照片上,她用一英寸代表5英尺。如果她的卧室墙长10英尺,Casey将用多少英寸图来代表这个测量?
  播放段落
  5. If two inches are equal to twelve feet, how many inches would be equal to 36 feet?
     ::如果两英寸等于12英尺, 多少英寸等于36英尺?
  播放段落
  6. If four inches are equal to sixteen feet, how many feet are two inches equal to?
     ::如果四英寸等于十六英尺,那么两英寸等于多少英尺?
  播放段落
  7. The carpenter chose a scale of 6" for every twelve feet. Given this measurement, how many feet would be represented by 3"?
     ::木匠每12英尺选择6英尺的尺码。根据这种测量,3英尺代表几英尺?”
  播放段落
  8. If 9 inches are equal to 27 feet, how many feet are equal to three inches?
     ::如果9英寸等于27英尺,多少英尺等于3英寸?
  播放段落
  9. If four inches are equal to 8 feet, how many feet are equal to two inches?
     ::如果四英寸等于八英尺, 多少英尺等于两英寸?
  播放段落
  10. If six inches are equal to ten feet, how many inches are five feet equal to?
      ::如果6英寸等于10英尺,那么5英尺等于多少英寸?
  播放段落
  11. If four inches are equal to twelve feet, how many inches are equal to six feet?
      ::如果四英寸等于十二英尺, 有多少英寸等于六英尺?
  播放段落
  12. For every 20 feet of fence, John drew 10 inches on his plan. If the real fence is only 5 feet long, how many inches will John draw on his plan?
      ::每20英尺的栅栏,约翰就在他的计划上画了10英寸。 如果真正的围栏只有5英尺长,那么约翰会用多少英寸来图画他的计划?
  播放段落
  13. If eight inches are equal to twelve feet, how many inches are equal to six feet?
      ::如果八英寸等于十二英尺, 有多少英寸等于六英尺?
  播放段落
  14. How many inches are equal to 20 feet if 4 inches are equal to 10 feet?
      ::如果4英寸等于10英尺,多少英寸等于20英尺?
  播放段落
  15. How many inches are equal to 8 feet if six inches are equal to 16 feet?
      ::如果6英寸等于16英尺,等于8英尺多少英寸?
  播放段落
  16. Nine inches are equal to twelve feet, so how many inches are equal to 4 feet?
      ::九英寸等于十二英尺, 多少英寸等于四英尺?
  播放段落
  17. If a person runs two miles in twelve minutes, how long will it take them to run 4 miles at the same rate?
      ::如果一个人在12分钟内跑两英里 他们要多久才能以同样的速度跑四英里?
  播放段落
  18. A person runs 1 mile in 16 minutes. Given this information, how long will it take him/her to run 3 miles?
      ::一个人在16分钟内跑1英里。根据这个信息,他/她要跑3英里需要多长时间?
  播放段落
  19. If a person runs two miles in twenty minutes, at what rate does he/she run one mile?
      ::如果一个人在20分钟内跑两英里 以什么速度跑一英里?

  播放段落

  Review (Answers) 
  ::回顾(答复)

  播放段落

  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 。

  播放段落

  Resources
  ::资源