# Two automobiles are travelling on intersecting roads at 35 km/h and 25 km/h. Assuming that these cars will continue at this rate, will they collide? Two automobiles are travelling on intersecting roads. The first automobile is travelling northeast at 35 km/h. The second automobile begins 7 km north of the first, and it is travelling east at 25 km/h. Assuming that these cars will continue at this rate, will they collide? Assign vector equations to each line and assume that the first automobile begins at the origin. We can model the roads with the following graph:

The first road heads northeast and goes through the origin (the origin is arbitary but we are told to put it where the first car starts driving).  That is the line `y=x`

The second car starts 7km north of the first, so that is the point (0,7) on our graph.  It travels east, so we can model that by the line `y=7`

The point of intersection is (7,7)

How long will it take each car to get there?

The distance from the origin to the point (7,7) is: `7sqrt(2)=9.8994949`

Traveling at 35kph, it...

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