Answer :
Answer:
10 miles.
Step-by-step 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:
[tex]\frac{\text{The sum distances of 5 races}}{5}=4[/tex]
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:
[tex]\frac{1+2+3+4+x}{5}=4[/tex]
[tex]\frac{10+x}{5}=4[/tex]
Let us multiply both sides of our equation by 5.
[tex]\frac{10+x}{5}*5=4*5[/tex]
[tex]10+x=20[/tex]
Let us subtract 10 from both sides of our equation.
[tex]10-10+x=20-10[/tex]
[tex]x=10[/tex]
Therefore, the maximum possible distance of Henry's longest race is 10 miles.