On a usual day, a man goes home from work by catching a train from Station A to Station B, then walks 10 minutes to go home.
Today, on his way back, the train stopped at Station K, located between A and B because of an accident ahead. He got down to the Station K and caught a taxi for home. The taxi took 30 minutes to arrived at his home. He looked at the clock and found that he was 5 minutes later than the usual day.
Question: What is the distance (in km) between Station K and his home?
Details and Assumptions:
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Let the distance between K and the man's home be x km. Then that between A and K is 3 x km. Let the speed of the train by v . Then that of the taxi is 2 v .
The time taken for the man to reach home from work is t usual = train v 4 0 + walk 1 0 minutes. Since today, he was 5 minutes late, t today = v 4 0 + 1 5 . This time is the same as t today = A-K v x / 3 + taxi v / 2 x . Therefore,
v 4 0 + 1 5 v 4 0 + 1 5 ⟹ v v 2 x ⟹ x = 3 v x + v 2 x = 5 + 3 0 = 2 = 3 0 = 3 0 Since taxi ride is v 2 x = 3 0 minutes