Question

After 3 hours, they are ____ miles apart. (Round to the nearest mile as needed.)

Answer 1

Since Mike drove at 65 mph for 3 hours, we have that he traveled:

$3\cdot65=195\text{ miles}$

for Sandra, we have the following:

$3\cdot70=210\text{ miles}$

notice that both trajectories with the distance apart segment form a right triangle, then, using the pythagoren theorem, we get:

$x=\sqrt[]{(210)^2+(195)^2}=\sqrt[]{44100+38025}=\sqrt[]{82125}\approx287\text{ miles}$

therefore, Sandra and Mike are approximately 287 miles apart after 3 hours