Jason swam 3 and one-half miles, then another 3 1/4th miles in one day. On the same day, Rachel swam 2 2/3rd miles, then another 4 and one-half miles. How many more miles did Rachel swim than Jason?
Accepted Solution
A:
Hello!The answer is:Rachel swam [tex]\frac{5}{12}[/tex] miles or 0.42 miles more than Jason.Why?To calculate how many miles did Rachel swim more than Jason, we need to write the following equation:[tex]Difference=RachelMiles-JasonMiles[/tex]Where,Difference, is equal to the number of Miles that Rachel did more than JasonRachelMiles, is equal to 2 2/3rd miles plus 4.5 miles.Jason Miles, is equal to 3.5 miles plus 3 1/4th miles.Also, we need to remember the following: - How to convert mixed fractions to improper fractions,[tex]a\frac{b}{c}=a+\frac{b}{c}[/tex] - How to add or subtract fractions and whole numbers.[tex]a+\frac{b}{c}=\frac{ac+b}{c}[/tex]Now, we are given the following information:Jason's miles:[tex]JasonMiles=3\frac{1}{2}+3\frac{1}{4} =(3+\frac{1}{2})+(3+\frac{1}{4})\\\\JasonMiles=(3+\frac{1}{2})+(3+\frac{1}{4})=(\frac{(2)*(3)+1}{2})+(\frac{(3)*(4)+1}{4})\\\\JasonMiles=(\frac{(2)*(3)+1}{2})+(\frac{(3)*(4)+1}{4})=\frac{7}{2}+\frac{13}{4}\\\\JasonMiles=\frac{(7)*(4)+(2)*(13)}{8}=\frac{28+26}{8}=\frac{54}{8}\\\\JasonMiles=\frac{54}{8}=\frac{27}{4}miles[/tex]Rachel's miles:[tex]RachelMiles=2\frac{2}{3}+4\frac{1}{2}=(2+\frac{2}{3})+(4+\frac{1}{2})\\\\RachelMiles=(2+\frac{2}{3})+(4+\frac{1}{2})=(\frac{(2)*(3)+2}{3})+(\frac{(4)*(2)+1}{2})\\ \\RachelMiles=(\frac{(2)*(3)+2}{3})+(\frac{(4)*(2)+1}{2})=\frac{6+2}{3} +\frac{8+1}{2}\\\\RachelMiles=\frac{6+2}{3} +\frac{8+1}{2}=\frac{8}{3}+\frac{9}{2}\\\\RachelMiles=\frac{8}{3}+\frac{9}{2}=\frac{(8)*(2)+(3)*(9)}{(3)*(2)}\\\\RachelMiles=\frac{(8)*(2)+(3)*(9)}{(3)*(2)}=\frac{16+27}{6}=\frac{43}{6}miles[/tex]Now, substituting the miles swam by Rachel and Jason into the equation, we have:[tex]Difference=\frac{43}{6}-\frac{27}{4}=\frac{(43)*(4)-(6)*(27)}{24}\\\\Difference=\frac{(43)*(4)-(6)*(27)}{24}=\frac{172-162}{24}\\\\Difference=\frac{172-162}{24}=\frac{10}{24}=\frac{5}{12}miles=0.42miles[/tex]Hence, we found that Rachel swam 0.42 miles more than Jason.Have a nice day!