Question

Henry ran five races, each of which was a different positive integer number of

miles. The mean of his distances was 4 miles. What is the maximum possible distance
of his longest race?

Answer 1

10 miles.

Explanation:

Let x be the number of miles on Henry's longest race.

We have been given that Henry ran five races, each of which was a different positive integer number of miles.

We can set an equation for the average of races as:

`\frac{\text{The sum distances of 5 races}}{5}=4`

As distance covered in each race is a different positive integer, so let his first four races be 1, 2, 3, 4.

Now let us substitute the distances of 5 races as:

`(1+2+3+4+x)/(5)=4`

`(10+x)/(5)=4`

Let us multiply both sides of our equation by 5.

`(10+x)/(5)*5=4*5`

`10+x=20`

Let us subtract 10 from both sides of our equation.

`10-10+x=20-10`

`x=10`

Therefore, the maximum possible distance of Henry's longest race is 10 miles.