Tyrell exercised this week both by walking and by biking. He walked at a rate of 4 mi/h and biked at a rate of 12 mi/h. The total distance he covered both walking and biking was 36 miles and Tyrell spent one more hour walking than biking.

A. Define a variable and write an equation for this solution.

B. How many hours did Tyrell spend on each activity?

A. The equation is 4 (t + 1) + 12t = 36

B. He spent 2 hours on biking and 3 hours on walking

Step-by-step explanation:

* Lets explain how to solve the problem

- Tyrell walked at a rate 4 miles per hour

∴ His speed on walking is 4 miles/hour

- Tyrell biked at rate 12 miles per hour

∴ His speed on biking is 12 miles/hour

- The total distance he covered both walking and biking was

36 miles

- Assume that he walked x and biked y

∴ x + y = 36 ⇒ (1)

- Tyrell spent one more hour walking than biking

- Assume that he biked for t hours

∵ He walked one more hour than he biked

∵ He biked for t hours

∴ He walked for t + 1 hours

A.

∵ Distance = speed * time

∴ x = 4 * (t + 1)

∴ x = 4 (t + 1)

∴ y = 12 * t

∴ y = 12t

- Substitute x and y in equation (1)

∴ 4 (t + 1) + 12t = 36 ⇒ the equation

B.

* Lets solve the equation

- Multiply the bracket by 4

∴ 4t + 4 + 12t = 36

- Add like terms in left hand side

∴ (4t + 12t) + 4 = 36

∴ 16t + 4 = 36

- Subtract 4 from both sides

∴ 16t = 32

- Divide both sides by 16

∴ t = 2

∵ t represents the time of biking

∴ He biked for 2 hours

∵ t + 1 represents the time of walking

∵ t + 1 = 2 + 1 = 3

∴ He walked for 3 hours