Solving Using Substitution

Substitution

Example 2

Peter and Nadia like to race each other. Peter can run at a speed of 5 feet per second and Nadia can run at a speed of 6 feet per second. To be a good sport Nadia likes to give Peter a head start of 20 feet. How long does Nadia take to catch up with Peter? At what distance from the start does Nadia catch up with Peter?

Step 1. Write a linear equation to represent each person in the situation.

Nadia's equation d= 6t

Peter's equation d = 5t + 20

Step 2. Isolate one variable in one equation.

In this example both equations have d isolated.

Step 3. Substitute the isolated variable's equivalent expression into the other equation.

6t = 5t + 20

Step 4. Solve the remaining equation.

6t = 5t + 20

t = 20

Step 5. Substitute the value of the variable found in step 3, into either equation to find the other variable.

d = 6t

d = 6(20)

d = 120

Nadia and Peter meet 20 seconds after they start racing,
at a distance of 120 yards away.