Answer:
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