Algebra Problems, Math Problems

Problem of the Day: 1/12/13

What is the sum of the solutions of ||x-1|-2|=1?

Solution to yesterday’s problem:

First of all, we should express the distance traveled by each car using the distance formula d=rt. The red car’s speed (r) is 60mph, and the time it travels is our variable, t; so the red car’s distance is 60t. Doing likewise for the blue car, we find that the other car’s distance is 80t. We can use t in both expressions because each car travels for the same amount of time.

The red car is traveling north, and the blue car is traveling east, so the distance between them would be the hypotenuse of a right triangle. We can express the problem using the Pythagorean theorem:

(60t)^2+(80t)^2=(200)^2

Remember, we’re trying to find the time when the distance is 200 miles. So all we need to do to solve this problem is simplify this equation. Simplifying the exponents,

3600t^2+6400t^2=40000

Combining like terms,

10000t^2=40000

Taking the square root of both sides,

100t=200

t=2

So the two cars will be 200 miles apart after 2 hours.

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s