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 $4\frac{1}{3}$ miles, $3\frac{1}{2}$ miles, $3\frac{5}{6}$ miles, $4\frac{1}{6}$ miles.

We have to find the average distance for 4 days.

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

$4\frac{1}{3} =\frac{(4)(3)+1}{3} =\frac{12+1}{3} =\frac{13}{3}$

$3\frac{1}{2}=\frac{(3)(2)+1}{2} =\frac{6+1}{2} =\frac{7}{2}$

$3\frac{5}{6} =\frac{(3)(6)+5}{6}=\frac{18+5}{6}=\frac{23}{6}$

$4\frac{1}{6} =\frac{(4)(6)+1}{6}=\frac{24+1}{6} =\frac{25}{6}$

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

By adding the distances we will get,

$\frac{13}{3} +\frac{7}{2} + \frac{23}{6} +\frac{25}{6}$

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 $\frac{13}{3}$  as 6 we will multiply the numerator and denominator both by 2. We will get,

$\frac{(13)(2)}{(3)(2)} =\frac{26}{6}$

Similarly, $\frac{7}{2} =\frac{(7)(3)}{(2)(3)} =\frac{21}{6}$

$\frac{26}{6} +\frac{21}{6} +\frac{23}{6}+\frac{25}{6}$

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

$\frac{(26+21+23+25)}{6}$

= $\frac{95}{6}$

Now the average distance

= $\frac{\frac{95}{6}}{4}$

= $(\frac{95}{6})(\frac{1}{4})$

= $\frac{(95)(1)}{(6)(4)}$

= $\frac{95}{24}$

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

$\frac{95}{24} =\frac{(3)(24)+23}{24} = 3\frac{23}{24}$

So we have got the required answer.

The average distance is $3\frac{23}{24}$ miles.