Question

(a) write an equation and (b) solve.

1. ed spent 2 hr. less time working on his science fair project this week than last. if he worked a total of 8 hr. on his project during both weeks, how long did he work on his project this week?

Explanation:

Step1: Define Variables

Let \( x \) be the time (in hours) Ed worked on his project last week. Then, the time he worked this week is \( x - 2 \) hours.

Step2: Set Up Equation

The total time for both weeks is 8 hours. So, the equation is \( x+(x - 2)=8 \).

Step3: Solve the Equation

Simplify the left - hand side: \( x+x - 2=8\Rightarrow2x-2 = 8 \).
Add 2 to both sides: \( 2x-2 + 2=8 + 2\Rightarrow2x=10 \).
Divide both sides by 2: \( x=\frac{10}{2}=5 \).
Now, find the time for this week: \( x - 2=5 - 2 = 3 \) hours.

Answer:

(a) The equation is \( x+(x - 2)=8 \) (where \( x \) is the time last week in hours). (b) Ed worked 3 hours on his project this week.