Solving for x: A Narrow Bridge Challenge

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To solve the problem of crossing a 1km bridge before being hit by a truck traveling at 90km/h, one must express the time needed to reach either end of the bridge as a function of the distance from the far end, x. The truck's time to reach the end of the bridge can be calculated based on its speed. The key is to set the time it takes for the runner to reach the end equal to the time it takes for the truck to reach the same point. There are two possible distances from the far end where the runner can safely escape before the truck arrives. Understanding these calculations is crucial for determining the safe distance.
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Homework Statement



You are crossing a narrow bridge 1km long when you notice a truck approaching at 90km/h. If you can run at 5m/s, how far from the far end must you be if you could reach either end just before being hit by the truck?

2ltgg1j.jpg


My attempt

Displacement between the two: 1000 - x + d
When displacement is 0, they will meet? I can't seem to solve for x... I end up with more variables than I have equations. :S
 
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Express the time you need to reach bridge end as a function of x, calculate the time truck needs to reach the end of the bridge. If truck needs more time, you will make it.

Note that there are two answers to the question.
 

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