Two cars leave an intersection at the same time. One travels north and the other travels east. When the eastbound car is 1 mile further than the northbound car from the intersection, the distance between them is 2 miles more than the northbound car's distance from the intersection. How far is the northbound car from the intersection?

Question

Two cars leave an intersection at the same time. One travels north and the other travels east. When the eastbound car is 1 mile further than the  northbound car from the intersection, the distance between them is 2 miles more than the northbound car's distance from the intersection. How far is the northbound car from the intersection?

anonymous · Answer

use the pythagoras theorem :$$c^2 = x^2 + y^2$$

where c = 2 miles
          x = 1 mile

so plug this in the theorem and you'll get the following:

$$(2)^2 - 1 = y^2$$
$$y = \sqrt(4-1) \rightarrow y = \sqrt(3)$$

I think so, correct me if I'm wrong ^_^

anonymous · Answer

I think you made a mistake :)

anonymous · Answer

I concur.

anonymous · Answer

If the distance of the northbound car from the intersection point is x, then the distance of the eastbound car from the intersection is y+1, and the distance between the two cars is 2+y.

anonymous · Answer

So,
$$(2+y)^2=y^2+(y+1)^2$$

anonymous · Answer

Solve the quadratic equation, you get y=-1 or y=3. Take only the positive value of y. Therefore the northbound car is 3 miles away from the intersection.

anonymous · Answer

I should go prepare for my exam, or I am definitely getting a very bad grade.

anonymous · Answer

why is it 2 + y?

anonymous · Answer

oh, right, nvm lol, I again misread the question, sorry ^_^"