Problema Solution
Joe’s wife drives him to the train station where he catches the train to work everyday. At the end of the day, Joe rides the train back to the station where his wife meets him and drives him home. One day, Joe decides to leave work early. Arriving at the train station one-hour early and not wanting to disturb his wife, he begins walking home when he arrives at the station. His wife leaves home at the usual time. On her way to the station, she sees Joe walking along the road. She turns around, picks him up, and they arrive home 20 minutes earlier than usual. How long was Joe walking?
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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 20 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-10)--------------(2t-20)
wife leaves at 0 again
return time = 2t-20
pick up time = t-10 (halfway)
:
Walking time = pick-up time - start time
Walking time = (t-10) - (t-60)
Remove brackets: t - 10 - t + 60 = 50 min spent walking