Every day a commuter takes a train that arrives at her station at precisely 6:00 pm. She is met at the station by her husband, who also arrives at precisely 6:00 pm. He always drives the same route to the station and never varies his speed. One day the commuter takes and earlier train and arrivds at the station at precisely 5:00 pm. She dicides to begin walking home along her husband's usual route. They meet, she gets into the car, and they drive home. They arrive home precisely ten minutes earlier than usual. How long had the commuter been walking?
50 minutes
1:00
55 minutes. It is checked.
To determine how long the commuter had been walking, we need to find the time difference between her arrival at the station and her normal arrival time with her husband. Let's break down the information given:
1. The normal arrival time at the station for both the commuter and her husband is precisely 6:00 pm.
2. The commuter takes an earlier train and arrives at the station at precisely 5:00 pm.
3. After her early arrival, the commuter starts walking home along her husband's usual route.
4. They meet on their usual route, and the commuter gets into the car to drive home with her husband.
5. They arrive home precisely ten minutes earlier than usual.
To solve this problem, let's consider the time it takes for the husband to drive the usual route. Since the husband never varies his speed, it implies that the travel time from the station to their home is constant. Let's assume this travel time is 'x' minutes.
The time the husband usually spends waiting at the station for his wife is 6:00 pm minus x minutes.
When the wife arrives at the station at 5:00 pm, she starts walking along her husband's route. At some point, they meet, and let's assume it happens after 'y' minutes of walking.
When they meet, the husband drives the remaining distance home with his wife. This distance takes 'x' minutes to cover, as mentioned earlier.
Considering the information that they arrive ten minutes earlier than usual, we can set up an equation:
Time husband waits at the station + Time wife spends walking + Time husband spends driving = Time saved (10 minutes)
(6:00 pm - x) + y + x = 10 minutes
Simplifying the equation, we can see that the husband's waiting time (6:00 pm - x) cancels out:
y + x = 10 minutes
Now we need to find the value of 'y,' which represents the time the commuter spends walking.
Since the commuter takes an earlier train, she spends an hour walking (60 minutes). This means that:
y + 60 minutes = 10 minutes
Subtracting 60 minutes from both sides of the equation:
y = -50 minutes
The value of 'y' is -50 minutes, which means the commuter had been walking for 50 minutes before meeting her husband.
Therefore, the answer is that the commuter had been walking for 50 minutes.