Alice walks on a straight line at four miles per hour. Two hours after she begins walking, Bob runs after her at a rate of six miles per hour. How fast (in miles per hour) is Bob gaining on Alice?
r = 6-4 = 2mi/h.
To find out how fast Bob is gaining on Alice, we need to calculate their relative speed. Relative speed is the difference between their individual speeds.
Alice walks at a speed of 4 miles per hour, and Bob runs at a speed of 6 miles per hour. Since their directions are the same (both on the straight line) and Bob is chasing Alice, we subtract Alice's speed from Bob's speed to find the relative speed.
Relative speed = Bob's speed - Alice's speed
Relative speed = 6 mph - 4 mph
Relative speed = 2 mph
Therefore, Bob is gaining on Alice at a speed of 2 miles per hour.