Question

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?

Answer 1

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