Question

Two cars start at the same point. One car starts out driving north at 25 mph. Two hours later the second car starts driving east at 20 mph. How long after the first car starts traveling does it take for the two cars to be 300 miles apart?

Answer 1

It takes 10.1 hrs after the 1st car for the two cars to be 300 miles apart

Explanation:

Given:

Two cars start out at the same point.

One car starts out driving north at 25 mph.

Two hours later the second car starts driving east at 20 mph.

To Find:

How long after the first car starts traveling does it take the two cars to be 300 miles apart?

Solution:

This is problem can be solved by using Pythagorean theorem

`a^2 + b^2 = c^2`

Let driving time of 1st car be t

then distance driven by the 1st car will be

= Speed X time

=25t

Let driving time of 2nd car be (t-2)

then distance driven by the 2nd car

= speed x time

= 20(t-2)

Now

`(25t)^2 + (20t-40)^2 = 300^2`

`625t^2 + (400t^2 - 1600t + 1600) = 90000`

`625t^2 + 400t^2 - 1600t + 1600 - 90000 = 0`

1025t^2 - 1600t - 88400 = 0

divide the equation by 25

`41t^2 - 64t - 3536 = 0`

Solving this equation using the quadratic formula; a=41; b=-64; c=-3536

The positive solution will be x = 10.1 hrs after the 1st car departs