Question

van departs due north at 20 mph, starting at the same point and in the same line, bicycles due east at 15 mph. diagram: compass (n, s, e, w) and a right - angle with van on vertical, bike on horizontal, not drawn to scale how far apart are they after 2 hours? options: a. 10 miles, b. 35 miles, c. 50 miles, d. 70 miles

Explanation:

Step1: Calculate distance of van

The van's speed is 20 mph, time is 2 hours. Using \( \text{distance} = \text{speed} \times \text{time} \), we get \( 20 \times 2 = 40 \) miles.

Step2: Calculate distance of bicycle

The bicycle's speed is 15 mph, time is 2 hours. Using \( \text{distance} = \text{speed} \times \text{time} \), we get \( 15 \times 2 = 30 \) miles. Wait, no—wait, the van and bicycle are moving in perpendicular directions (north and east, from the compass). So we use the Pythagorean theorem. Wait, no, maybe I misread. Wait, the problem says "starting at the same point and in the same line"? Wait, no, the diagram has north (van) and east (bike). So they are moving perpendicular. Wait, no, maybe the original problem: van goes north at 20 mph, bike goes east at 15 mph. Then after 2 hours, van has gone \( 20 \times 2 = 40 \) miles north, bike \( 15 \times 2 = 30 \) miles east. Then the distance between them is \( \sqrt{40^2 + 30^2} = \sqrt{1600 + 900} = \sqrt{2500} = 50 \) miles. So the correct answer is C. 50 miles.

Answer:

C. 50 miles