Question

A railroad and a highway intersect at right angles. A train is 10 miles from the intersection at the same moment that a car is 6 miles from the intersection. Both are traveling at 30 mph. How long until they are 4 miles apart?

Answer 1

After 12 minutes they will be 4 miles apart.

Explanation:

Since they are intersect in right angle, the distance between them is the hypotenuse of the triangle formed by them with intersection.

A train is 10 miles from the intersection at the same moment that a car is 6 miles from the intersection.Both are traveling at 30 mph.

Let the time when distance between them is 4 miles be t.

Distance to intersection for train = 10 - 30 t

Distance to intersection for car = 6 - 30 t

We know that hypotenuse is 4 miles that is

`4=√((10-30t)^2+(6-30t)^2)\\\\16=(10-30t)^2+(6-30t)^2\\\\16=100-600t+900t^2+36-360t+900t^2\\\\1800t^2-960t+120=0\\\\\texttt{t=0.333hr or t = 0.2hr}`

Consider the smallest time, t = 0.2 hr = 12 minutes

After 12 minutes they will be 4 miles apart.