Yeah it's a typo. Remember that English is not my native language
Although Advong says he doesn't fully understands why, he has the correct answer.
There are a few things you can tell:
He normally doesn't arrive at home before 18:00, so in this example he cannot arrive before 17:50 (as he is 10 minutes earlier than normal)
So therefore, the walk simply cannot take less than 50 minutes. that's a fact.
But he started walking to catch his wife to pick him up. His wife needs to travel towards the station and the time it takes is the same time it takes to return home.
And there are no such things as traffic jams etc in riddles :P
Fact is that he caught his wife on 50% of the distance
driven by the time they got home.
The time they gained at the end is 10 minutes, so he caught his halfway of that advantage and therefore gained another 5 minutes, which makes 55 minutes.
To prove my theory here are some examples:
Y=meeting time
10 minute drive from the station
1. 17:50 (she leaves home)
2. Y
3. 18:00 + 10 - 10 = 18:00
Y = 17:50 + (10min / 2) = 17:55
34 minute drive
1. 17:26
2. Y
3. 18:00 + 34 - 10 = 18:24
Y = 17:26 + (58 /2) = 17:26 + 29 = 17:55
For those who don't really like the formula-like notation here's a more story-like one :P
Imagine it takes 30 minutes to go to the station to pick up johnny, then the wife has to leave home at 17:30
To get home 10 minutes earlier than normal they would have to arrive at 18:20.
Johnny has to catch his wife halfway her ride so that would be at 17:55 which is 55 minutes after his arrival at the station.
If it takes 60 minutes to drive to the station she would have to leave at 17:00 and their normal time of arrival would be at 19:00. To be ten minutes early, they would have to arrive at 18:50.
1:50 / 2 = 55 minutes.
You can use any time and it will give the same result.
Anyway, Advong is the winner so here's the cookie
I'd rather have a bottle in front of me than a frontal lobotomy