Expert: Bobby Soltani - 7/9/2009

Question
Avoiding a Collision
A car is traveling on a road that is perpendicular to a railroad track.  when the car is 30 meters from he crossing the car's new collision detector warns the driver that there is a train 50 meters from the car heading toward the same crossing.  How far is the train from the crossing.  

Answer
40 meters. The hint is that the road is perpendicular to the track, so you're working with a right triangle. It may help if you draw it.

The car is 30 meters from the crossing, which makes the car-to-track line one of the sides on the square corner of your right triangle. The other side is the train-to-crossing distance, which is what we're trying to figure out.

The train is 50 meters from the car, which is the hypotenuse of the right triangle.

Now plug the numbers into the Pythagorean Theorem formula A^2 + B^2 = C^2, where C is the hypotenuse (50 meters) and A is the side whose length you already know (30 meters). Then solve for B using algebra:

30^2 + B^2 = 50^2
900 + B^2 = 2500
B^2 = 1600
B = 40

Another trick is to remember the 3-4-5 right triangle. When you multiply the lengths of the sides by 10, you have 30-40-50, which is the exact same triangle in your word problem. When I saw that, I knew the train was 40 meters from the crossing without even having to do the algebra.

Good luck,

Bobby