Problem Solving: Work Backward

Will arrived at his mother's office at 3 p.m. It took him 30 minutes to walk from his home to the mall. He was in the mall for 45 minutes. It them took him 15 minutes to walk to his mother's office. At what time did Will leave home?

30 + 45 + 15 = 1 1/2 hours

He left home at 1:30

To solve this problem using the work backward strategy, we will start by figuring out the time Will arrived at his mother's office and work our way backward to determine the time he left home.

Given information:
- Will arrived at his mother's office at 3 p.m.
- It took him 30 minutes to walk from home to the mall.
- He was in the mall for 45 minutes.
- It took him 15 minutes to walk from the mall to his mother's office.

Let's work backward:

1. We know that Will arrived at his mother's office at 3 p.m., and it took him 15 minutes to walk from the mall to the office. Therefore, he left the mall at 3 p.m. - 15 minutes = 2:45 p.m.

2. We also know that it took him 45 minutes to be in the mall. So, if he left the mall at 2:45 p.m., he must have entered the mall at 2:45 p.m. - 45 minutes = 2:00 p.m.

3. Lastly, we know that it took him 30 minutes to walk from home to the mall. So, if he entered the mall at 2:00 p.m., he must have left home at 2:00 p.m. - 30 minutes = 1:30 p.m.

Therefore, Will left home at 1:30 p.m.