# 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.