Question

1. Kate ran 6 miles more than Peter ran. The sum of their distances is 28 miles. How far did Peter run? The domain of the solution is {0, 6, 11, 24}.
a. Define your variable.
b. Write algebraic expressions for the distances each person ran.
c. Write an equation that can help you solve the problem.
d. Solve the equation.
e. Check your answer.

Answer 1

You have to create equations.

Kate ran 6 miles more than Peter ran.

so an equation would be K=6+P

The sum of their distances is 28 miles

so an equation would be K+P=28

P=?

Now use substitution.

K+P=28

since K=6+P then P=K-6. Plug this in.

K+(K-6)=28

2K-6=28

2K=34

K=17

Now that we know how far Kate ran. We can figure out how far Peter ran.

K+P=28

17+P=28

P=11

Peter ran 11 miles.