A wife picks up her husband after work at a certain hour eve

A wife picks up her husband after work at a certain hour every day. (It takes the same amount of time to drive there as it does to drive back.) One day, her husband gets off work an hour early, so he stars walking. His wife leaves at her usual time and finds him along the way. THey arrive back home 30 minutes earlier than usual. How long did her husband spend walking?

Solution

A wife picks up her husband after work at a certain hour every day.
(It takes the same amount of time to drive there as it does to drive back.)
One day, her husband gets off work an hour early, so he starts walking.
His wife leaves at her usual time and finds him along the way.
They arrive back home 30 minutes earlier than usual.
How long did her husband spend walking?
:
Use a time line, where t = time of normal one-way trip to pick-up
Start time from home = 0, returns at 2t
:
Normal day: 0--------------------t--------------------2t(return home)
:
:
walks 60 min before t: (t-60)---------0----------(t-15)--------------(2t-30)
wife leaves at 0 again
return time = 2t-30
pick up time = t-15 (halfway)
:
Walking time = pick-up time - start time
Walking time = (t-15) - (t-60)
Remove brackets: t - 15 - t + 60 = 45 min spent walking