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3. To break the school's record, the girls' time had to be faster than 12 2/5minutes. Did the girls break the record? If so, how much faster werethey? If not, how much slower were they?

3. To break the school's record, the girls' time had to be faster than 12 2/5minutes-example-1
User Gwendal
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1 Answer

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15 votes

ANSWER

The girls did not break the record

Explanation:

Given information


\begin{gathered} Barbara\text{ spent }3(3)/(10)\text{ minutes to complete the relay race} \\ \text{Donna spent 2}(4)/(5)\text{ minutes to complete the relay race} \\ \text{ Cindy spent x minutes to complete the relay race} \\ \text{ Nicole spent }2(1)/(10)\text{ minutes to complete the relay race} \end{gathered}

From the question provided, the record set by the school is 12 2/5 minutes

The next step is to find the time spent by Cindy in the relay race


\begin{gathered} 3(3)/(10)\text{ + 2}(4)/(5)\text{ + x + 2}(1)/(10)\text{ = 12}(2)/(5) \\ \text{The next process is to convert the mixed fraction into an improper fraction} \\ (33)/(10)\text{ + }(14)/(5)\text{ + x + }(21)/(10)\text{ = }(62)/(5) \\ \text{let the co}mmon\text{ denominator be 10} \\ \frac{33\text{ + 14(2) + 10x + (21})}{10}\text{ = }(62)/(5) \\ \frac{33\text{ + 28 + 10x }+\text{ 21}}{10}\text{ = }(62)/(5) \\ \frac{82\text{ + 10x}}{10\text{ }}\text{ = }(62)/(5) \\ \text{Cross multiply} \\ 5(82\text{ + 10x) = 62 }*10 \\ 410\text{ + 50x = 620} \\ \text{subtract 830 from both sides} \\ 410\text{ - 410+ 50x = 620 - 4}10 \\ 50x\text{ = 210} \\ \text{Divide both sides by 50} \\ (50x)/(50)\text{ = }(210)/(50) \\ x\text{ = }(21)/(5) \\ x\text{ = 4}(1)/(5)\text{ minutes} \end{gathered}

The next step is to sum all the minutes spent in the relay race


\begin{gathered} \text{Total minutes =}(33)/(10)\text{ + }\frac{14}{5\text{ }}+(21)/(5)+\text{ }(21)/(10) \\ \text{Total minutes = }\frac{33\text{ + 28 + 42 + 21}}{10} \\ \text{Total minutes = }(124)/(10) \\ \text{Total minutes = 12}(4)/(10)\text{minutes} \end{gathered}

From the above calculations, you will see that the girls ran a total of minutes of 12 4/10 minutes

Therefore, the girls did not break the record

User Nino Van Der Mark
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