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John's Train Is on Time

A train leaves on time. After it has gone 8 miles (at 33mph) the driver looks at his watch and sees that the hour hand is exactly over the minute hand. When did the train leave the station?

Speedy Sidney

Age 11 to 14
Challenge Level

The problem can be solved by considering the relative speed of the trains.

The speed of approach of the trains is 125 km/h on a 100 km track, so they will collide after a time 100/125 = 4/5 hour. Sidney flies at 100 km/h for 4/5 hour so he flies 80 km.

Finally, if Sidney were to fly exactly 100 km, the relative speed of the trains would be 100 km/h, provided Sidney was continuing to fly at 100 km/h. OR ..... there is another way - do you have any suggestions?

We received the correct solutions from: Stephen Smith(South Greenhoe Middle School).