Question

Angela is riding her dirt bike along a trail. She traveled 24 miles north then traveled 13 miles east. Shestopped for a moment and noticed her bike had only enough gas to travel 30 miles. Angela needs toget back before she runs out of gas. She can either ride her bike back the way she came or take a straight path towards her starting point

Answer 1

The given path can be illustrated in the following diagram:

She has only 30 miles worth of gas, if she comes back through the same path then the total distance is:

$\text{Total distance=13 miles + 24 miles = 37 miles}$

Therefore, she has not enough gas to go back using the same path.

Now, the total distance traveled in a straight path (SP) can be found using the Pythagorean theorem, we get:

$\begin{gathered} SP=\sqrt[]{13^2+24^2} \\ SP=\sqrt[]{745} \\ SP=27.3\text{ miles} \end{gathered}$

Therefore, she needs to take a straight path.