Mismi and the Professor:
TTH: "
She spent 20 minutes less in driving time, 10 minutes each way, which means he walked 50 minutes?
Now, I thought the answer was 50 minutes; but 20 + 10 + 10?
TTH II:
"Say mismi normally meets the professor at 1:00. He arrived an hour early, meaning 12:00, and started to walk. He sees her at 12:50 (that accounts for 10 minutes early arrival and 10 minutes early back home for a total of 20 minutes). Since he started to walk at 12:00 and they came across one another at 12:50 that means he walked 50 minutes.
YES! You have it, and it is difficult to explain
It will help if you draw a graph...
Suppose another couple (call them couple B) lives with the couple stated in the problem (call them couple A). Normally both men catch the same train home. However today the husband B arrives at the station 20 minutes early and wife B is already there to take him home. Both men will arrive home at the same time, because both arrive 20 minutes earlier than usual.
On their way home at some point couple B will pass wife A picking up husband A and they will drive the rest of the way home side by side, again both arriving 20 minutes early.
Now assume that wife A didn't see her husband and instead kept going to the train station. She would have arrived exactly 20 minutes after wife B left, because husband B arrived 20 minutes before husband A was expected to arrive, and wife A is always exactly on time. Likewise if wife B had turned around when she saw husband A and went back to the station she would have arrived 20 minutes after she left the station.
In other words it would take her 10 minutes to reach husband A and 10 minutes to get back to the station.
So after A walked for 40 minutes wife B would have left the station. 10 minutes later she would have caught up to husband A. So husband A walked a total of 50 minutes.
This problem comes from Games for the Super-Intelligent by James F. Fixx, which is out of print. - Congrats to S-I TTH.
Slippy writes, "
goodness knows what the Professor did in those 40 minutes but TTH lives within walking distance."
Oh my! Is that how TTH knew all about the times!!! Who would have thought it? :wink: