word problem for algebra

Question

Two cars leave an intersection. One car travels north: the other east. When the car traveling north had gone 15 miles, the distance between the cars was 5 miles more than the distance traveled by the car heading east. How far had the eastbound car traveled?

Answer 1

Final answer: 20 miles.

Solution: Whenever you can, draw a simple diagram using the information given in the problem. This problem gives you enough information to construct a right triangle and solve the problem using the Pythagorean theorem. Your diagram should have the North car's distance travelled as side "a" = 15 miles, the East car's distance (what we are solving for) as side "b" = x, and the distance between the two cars as the hypotenuse "c" = x + 5.

Substitute the values for a, b, and c into the Pythagorean theorem, which is a² + b² = c². You should then get 15² + x² = (x + 5)². FOIL and simplify as much as you can and you should get 225 + x² = x² + 10x + 25. Now try to get all the variables on one side of the equation and the numbers on the other side by adding and subtracting. x² gets cancelled out since x² - x² = 0, and 225 - 25 = 200, and 10x stays the same since no other terms have a singular "x" in them. Now you should get 10x = 200. At this point you want to isolate x in order to solve for it, and you can do this by simply dividing by 10 on both sides. Your final answer will be x = 20, so the The East car's distance (aka side "b") is 20 miles.

*Helpful Tip: You can check your answer by substituting the variable with your numerical answer and seeing if the values on both sides of the equation are the same. For instance, when we substitute 20 back into our Pythagorean theorem equation, we get 15² + 20² = (20 + 5)² which when we multiply it all out we get 625 = 625, so that checks out.

Hope this was helpful!

Answer 2

The distance travelled north (15) and east (call it x) are the legs of a right triangle. The distance between them is the hypotenuse of the right triangle which is x+5.

We can solve for x using the Pythagorean Theorem: x^2 + 15^2 = (x+5)^2

Which results in x = 28, so the east bound car had travelled 28 miles.