Question

math carver jogs 4 times a week. last week his distance were 4 1/3, 3 1/2, 3 5/6 abd 4 1/6, all measured in miles. what was the carvers average distance for the 4 days? express your answer as a mixed number

Answer 1

Given, Math Carver jogs 4 times a week.

Last week the distance which he covered are
`4(1)/(3)` miles,
`3(1)/(2)` miles,
`3(5)/(6)` miles,
`4(1)/(6)` miles.

We have to find the average distance for 4 days.

We have to convert the mixed fractions to improper fraction first.

`4(1)/(3) =((4)(3)+1)/(3) =(12+1)/(3) =(13)/(3)`

`3(1)/(2)=((3)(2)+1)/(2) =(6+1)/(2) =(7)/(2)`

`3(5)/(6) =((3)(6)+5)/(6)=(18+5)/(6)=(23)/(6)`

`4(1)/(6) =((4)(6)+1)/(6)=(24+1)/(6) =(25)/(6)`

Now to find average we have to add them and divide it by 4.

By adding the distances we will get,

`(13)/(3) +(7)/(2) + (23)/(6) +(25)/(6)`

To add them first we have to make common denominator. Here the denominators are 3, 2, 6, 6. So we can check the common denominator is 6 here.

To make the denominator of
`(13)/(3)` as 6 we will multiply the numerator and denominator both by 2. We will get,

`((13)(2))/((3)(2)) =(26)/(6)`

Similarly,
`(7)/(2) =((7)(3))/((2)(3)) =(21)/(6)`

`(26)/(6) +(21)/(6) +(23)/(6)+(25)/(6)`

As the denominators are same we will add the numerators. We will get,

`((26+21+23+25))/(6)`

=
`(95)/(6)`

Now the average distance

=
`((95)/(6))/(4)`

=
`((95)/(6))((1)/(4))`

=
`((95)(1))/((6)(4))`

=
`(95)/(24)`

We have got the average distance in improper fraction. We will convert it to mixed fraction.

`(95)/(24) =((3)(24)+23)/(24) = 3(23)/(24)`

So we have got the required answer.

The average distance is
`3(23)/(24)` miles.