# The Train and The Cyclist [closed]

A railway track runs parallel to a road until a bend brings the road to a level crossing. A cyclist rides to work along the road everyday at a constant speed of 12 miles per hour.
He normally meets the train that travels in the same direction at the crossing.
One day he was late by 25 minutes and met the train 6 miles ahead of the crossing.
Figure out the speed of the train

• Why is this question closed if it has a positive vote record and also required logical deduction? It is not textbook style Jan 4 '20 at 15:24

The train is travelling at:

72 miles per hour.

Working:

The train reaches the crossing at some time t. The cyclist is 25 minutes late, so he'll reach that point at t+25min. He travels 1 mile in 5 minutes, so at t he's 5 miles back. The train and cyclist met 6 miles before the crossing. Therefore at time t, in the same time it took the cyclist to travel 1 mile, the train went 6 miles. The cyclist's 12mph is 1 mile per 5 minutes; so the train travelled 6 miles in 5 mins, or 6*12 = 72mph.

An alternate approach:

The cyclist has half an hour (6 miles divided by 12 miles per hour gives 0.5 hour), or 30 minutes, to go to the crossing (on that day when he was late). Since he is late by 25 minutes, he is usually 5 minutes away from the crossing at that moment (when the train is 6 miles away from the crossing). So, this means that the train travels 6 miles per 5 minutes, or 6 miles per hour / 5 minutes * 60 minutes in an hour = 72 miles per hour.

• This could work as well! Jan 3 '20 at 8:48
• I request you to vote to reopen this question Jan 6 '20 at 17:57
• @Quark-epoch If the question is closed, it doesn't mean that it's bad. Actually, your question is very good (I've upvoted it). The only thing is that it's in the place which is a bit wrong for this kind of questions, since it's really textbook-style (I've personally encountered such problems many times, however, they're usually marked as higher-level ones). So, I believe that the question should be migrated to Math.SE. Jan 6 '20 at 18:59
• Yeah, I guess you are right in saying that. I never thought this would be called 'Textbook-Style' for my questions have also been closed for the same reason in the past and I didn't feel like it was one of them. Still, I think that this question should be migrated to Math.SE. Maybe I'll try doing that. Jan 9 '20 at 12:41