Question

A truck driver follows a road heading straight southwest. After 30 minutes, the driver finds that she is 20 km west from where she started and 15 km south. How far has she driven in a straight line?

A) 5 km
B) 25 km
C) 30 km
D) 35 km

Answer 1

Using the Pythagorean theorem, the straight-line distance the truck driver has driven is found to be 25 km, which corresponds to choice B in the provided options.

Step-by-step explanation:

To find out how far the truck driver has driven in a straight line, we can use the Pythagorean theorem because the driver's displacement forms a right-angled triangle with the legs being the westward and southward displacements. The distance to the west is one leg of the triangle, and the distance to the south is the other leg.

The formula for the Pythagorean theorem is:

a2 + b2 = c2

Where a and b are the legs of the triangle, and c is the hypotenuse or the straight-line distance driven by the truck. Plugging in the given distances into the formula:

(20 km)2 + (15 km)2 = c2

Solving for c:

(400 + 225) km2 = c2

625 km2 = c2

c = √(625 km2)

c = 25 km

Therefore, the truck driver has driven 25 km in a straight line.