# How long was Jack walking? - A visual solution.

## Problem:

Every day, Jack arrives at the railway station from work at 5 pm.
His wife leaves home in her car to meet him there at exactly 5 pm, and drives him home. One day, Jack gets to the station an hour early, and starts walking home, until his wife meets him on the road. They get home 30 minutes earlier than usual. How long was he walking?
Distances are unspecified. Speeds are unspecified, but constant.
Give a number which represents the answer in minutes.
Solution:
The best way to think about this problem is to consider it from the perspective of the wife. Her round trip was decreased by 30 minutes, which means each leg of her trip was decreased by 15 minutes.
Jack must have been walking for 45 minutes

## Exploring the visual solution

we can change the point of their meeting (i.e. the speeds of the two people). Highlight the point named 'Meeting Point' by clicking on it and use the arrow keys to move it.
We can also change the duration of the saved time.
Using this applet we can explore the outcomes of many scenarios of which a few are listed below.
1) If their meeting point is 1/4 th of the total distance (from the station to home) from the station, everyday at what time would Jack's wife leave her home to pick him up?
2) If Jack had been walking all the way to his home when would he reach his home?
3) If the average human walking speed at crosswalks is about 5 km/h, calculate the speed of the car that Jack's wife uses and also the distance between the Railway Station and Jack's home.

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