Section outline

  • Leaky Tanks
    ::轻型坦克

    Katie and Sunnie both have  20-gallon fish tanks  that are leaking water!  After 15 minutes, Katie's tank has leaked 4 3  gallon. After 20 minutes, Sunnie's tank has leaked 3 4  gallon. Which tank is leaking faster?
    ::凯蒂和逊尼派都有20加仑的鱼缸在漏水!15分钟后,凯蒂的坦克漏水43加仑。20分钟后,逊尼派的坦克漏水34加仑。哪个坦克漏水更快?

    Use the interactive to determine which tank is leaking faster.
    ::使用互动来确定哪个坦克漏水速度更快。

     

    INTERACTIVE
    Leaky Tanks
    minimize icon
    • Slide the red dot up and down to see how the water  levels change over time for each tank.
      ::向上和向下滑动红色点,看每个罐体的水位随时间变化。
    • Find the unit rate of leakage (in gallons per hour) for each tank.
      ::找出每辆坦克的单位渗漏率(每小时加仑)。
    • Determine which tank is leaking faster.
      ::确定哪个罐体漏水速度更快。
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    Progress
    0 / 5
    1.

    Select a unit rate that correctly describes the leak in Katie's tank.
    ::选择正确描述凯蒂坦克泄漏的单位费率 。

    a

    @$\begin{align*}\frac{1\text{ gallon}}{5 \tfrac{1}{3}\text{ hours}}\end{align*}@$
    ::@ $\ begin{ align@ frac{ 1\ text{ 加仑} 5\ tfrac{ 1\\\ 3} text{ hours{ end{ leign} $

    b

    @$\begin{align*}\frac{1.33 \text{ gallons}}{1 \text{ hour}}\end{align*}@$
    ::@ $\ begin{ align}\ frac{ 1. 33\ text{ 加仑{ 1\ text{ hour{ end{ ALign} $

    c

    @$\begin{align*}\frac{5.33 \text{ gallons}}{1 \text{ hour}}\end{align*}@$
    ::@ $\ begin{ align}\ frac{ 5. 33\ text{ 加仑{ 1\ text{ hour{ end{ ALign} $

    d

    @$\begin{align*}\frac{1 \text{ gallon}}{11.25\text{ minutes}}\end{align*}@$
    ::@ $\ begin{ align@ frac{ 1\ text{ 加仑} 11. 25\ text{ minutes{ end{ align} $

     

    Discussion Question
    ::讨论问题

    In this example, the units were the same. You were comparing gallons of water leaked per hour of two different tanks . But how could you compare if the  units  are different? 
    ::在这个例子中,单位是相同的。你比较了两个不同的罐子每小时漏水的加仑。但如果单位不同,你又如何比较呢?

     

    Which Leaks Faster?
    ::哪个漏水更快?

    Suppose  a blue container is leaking at a rate of 1 4  cup/min and a red container is leaking at 1 2  gal/hour. Which  container is leaking faster?
    ::假设蓝色容器漏水速度为14个杯子/分钟,红色容器漏水速度为12小时/小时。哪个容器漏水速度更快?

    Use the interactive below to compare the  leak rates  given different units.
    ::使用下面的交互效果比较不同单位的漏泄率 。

     

    INTERACTIVE
    Unit Conversions: Cups to Gallons
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    • Drag the red point to change the number of cups being converted.
      ::拖曳红色点以更改要转换的杯数 。
    • Note how the conversion factors are set up and which units are in the numerator and which are in the denominator.
      ::注意转换系数是如何设置的,在分子中是哪些单位,在分母中是哪些单位。

    The units are rounded to the nearest hundredths place.
    ::单位四舍五入到最近的一百个单位。

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    Relaxed Speed Reading
    ::放松的快速阅读

    After Katie and Sunnie fix the leaks in their tanks, they decide to relax by reading. Katie reads at a rate of  3 4  page per  2 3  minute. Sunnie reads at a rate of 18 pages per  1 4  hour. Who reads faster?
    ::凯蒂和逊尼派修补了他们的坦克漏水后,他们决定阅读放松。凯蒂的读数为每23分钟34页。逊尼派的读数为每14小时18页。谁读得更快?

    • Determine the unit rate for both girls in minutes
      ::在分钟内确定两个女孩的单位费率
    • Determine the unit rate for both girls in hours
      ::确定两个女孩工时的单位工资率

    Use the interactive to help answer the questions below .
    ::使用交互方式帮助回答下列问题。

     

    INTERACTIVE
    Reading Speeds
    minimize icon
    • Move the red point to determine the unit rate for both girls in minutes then in hours.
      ::将红点移开,以确定两个女孩的单位费率在分钟内,然后在小时内。
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       Summary
    ::摘要

    • In order to compare measures, they must be in the same units.
      ::为了比较措施,它们必须在同一单位。
    • Comparing rates is easiest when they are written as unit rates.
      ::比较率在以单位费率写成时最容易比较。
    • Multiplying or dividing two rates by the same number does not change whether one rate is greater or less than the other.
      ::乘以或除以相同数目的两种汇率,不改变一种汇率大于或低于另一种汇率。