Time and Train Waits for no Man

Algebra Level 3

A man cycles to work alongside a railway track. Everyday, he arrives at a railroad crossing exactly at the time that a train does. One day, the man is 50 minutes late and the train overtakes him 6 km from the crossing. If the man usually cycles at 6 km/h, in how many minutes will the train reach the crossing?

50 5 60 30 15 10

2 solutions

Ajit Athle
Jan 31, 2015

Let's say the man and the train normally reach the crossing at 9 a.m. Today since he's 50 minutes late, he'd reach it at 9:50 a.m. and thus when the train overtakes him, it would be 8:50 a.m. at 6 km before the crossing. The train would, of course, reach the crossing at 9 a.m. as usual. This means that the train travels at 6o km/h and would reach the crossing 10 minutes after overtaking the cyclist at 9 a.m. as usual.

Saya Suka
May 25, 2019

How true! Mom and I were left behind once before, and we never got to ride the ETS in the end. Haha, all this happen when the eki was just a kilometre away from our house.

On a usual day, both man and train simultaneously reach the station at time 0. On the special day, the train overtook him six km away from the station, which from his usual day POV, was where he would have been at time -60, that is an hour before his arrival (from his cycling speed of 6 km/h). Since we're told that he was 50 minutes late on this special day, so he should've been at time -10 on his daily routine, and just then he knew that the train would cover the six remaining km in ten minutes as they both arrive at the same time 0 as observed on a regular basis.

Time and Train Waits for no Man

2 solutions

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