Question

A car leaves a parking garage and travels 7 miles east. Then, the car turns left and travels 13 miles north. Now, it only has enough gas in the tank to travel 14.7 more miles. Can the car make it to the parking garage if it is able to take a direct route back? Justify your reasoning.

Answer 1

No. Read below.

Explanation:

If you graph this then you will see clearly.

Let's say the parking garage was at the origin. (0,0)

Then it goes to east to (7,0)

Then it goes north to (7,13)

Now if you connect the points, you'll see a triangle has formed. To figure out whether the car can make it back to the parking garage, you need to find out if the amount of miles left it can drive is greater than the hypotenuse or not. If it's greater, then it can make it home. If it is less, they're going to have to get some more fuel.

Using the Pythagorean Theorem, a²+b²=c² where a and b are the legs and c is the hypotenuse, we get:

7²+13²=c²

49+169=c²

c²=218

sqrt both sides

c=
`√(218)` ≈ 14.7648230602 So it will almost make it.