## Outline Mathematics

Algebra, Word problems

# Train on Bridge II

A train which is $180$ meters long passes a signal post in $90$ seconds. How long will it take for the train to cross a bridge that is $360$ meters long?

### Reference

- Sergey Dorichenko, A Moscow Math Circle: Week-by-Week Problem Sets (MSRI Mathematical Circles Library, 2012), #7.1

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A train which is $180$ meters long passes a signal post in $90$ seconds. How long will it take for the train to cross a bridge that is $360$ meters long?

### Solution

The train is moving at the rate of $2$ meters per second,meters per second,miles per hour because $2=$180/90,$360/180$,$180/90$. If so, the front of the train takes 360/2,$360/2$,$180/2$$=180$ seconds to cross the bridge. However, when this happens, the whole of the train has yet to leave the bridge, and this takes 90,$360$,$180$,$90$ (as if passing a signal post.) Therefore, it will take altogether 180+90,$360+90$,$180+90$,$90+90$ seconds between the train entering and leaving the bridge.

**Answer:** 270,$360$,$270$,$180$ seconds.

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