Question

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?

Answer 1

Hello!

The answer is:

Rachel swam
`(5)/(12)` 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:

`Difference=RachelMiles-JasonMiles`

Where,

Difference, is equal to the number of Miles that Rachel did more than Jason

RachelMiles, 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,

`a(b)/(c)=a+(b)/(c)`

- How to add or subtract fractions and whole numbers.

`a+(b)/(c)=(ac+b)/(c)`

Now, we are given the following information:

Jason's miles:

`JasonMiles=3(1)/(2)+3(1)/(4) =(3+(1)/(2))+(3+(1)/(4))\\\\JasonMiles=(3+(1)/(2))+(3+(1)/(4))=(((2)*(3)+1)/(2))+(((3)*(4)+1)/(4))\\\\JasonMiles=(((2)*(3)+1)/(2))+(((3)*(4)+1)/(4))=(7)/(2)+(13)/(4)\\\\JasonMiles=((7)*(4)+(2)*(13))/(8)=(28+26)/(8)=(54)/(8)\\\\JasonMiles=(54)/(8)=(27)/(4)miles`

Rachel's miles:

`RachelMiles=2(2)/(3)+4(1)/(2)=(2+(2)/(3))+(4+(1)/(2))\\\\RachelMiles=(2+(2)/(3))+(4+(1)/(2))=(((2)*(3)+2)/(3))+(((4)*(2)+1)/(2))\\ \\RachelMiles=(((2)*(3)+2)/(3))+(((4)*(2)+1)/(2))=(6+2)/(3) +(8+1)/(2)\\\\RachelMiles=(6+2)/(3) +(8+1)/(2)=(8)/(3)+(9)/(2)\\\\RachelMiles=(8)/(3)+(9)/(2)=((8)*(2)+(3)*(9))/((3)*(2))\\\\RachelMiles=((8)*(2)+(3)*(9))/((3)*(2))=(16+27)/(6)=(43)/(6)miles`

Now, substituting the miles swam by Rachel and Jason into the equation, we have:

`Difference=(43)/(6)-(27)/(4)=((43)*(4)-(6)*(27))/(24)\\\\Difference=((43)*(4)-(6)*(27))/(24)=(172-162)/(24)\\\\Difference=(172-162)/(24)=(10)/(24)=(5)/(12)miles=0.42miles`

Hence, we found that Rachel swam 0.42 miles more than Jason.

Have a nice day!