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?
6-4
You posted this yesterday
http://www.jiskha.com/display.cgi?id=1476153606
Why did you post it again today?
I trust Steve
To find how fast Bob is gaining on Alice, we need to calculate Bob's relative speed with respect to Alice.
We know that Alice walks at a constant speed of 4 miles per hour. After 2 hours, she will have already traveled a distance of 2 * 4 = <<2*4=8>>8 miles.
Now, let's consider Bob. He starts running after 2 hours, but Alice has already covered 8 miles during that time. So, Bob needs to cover this 8-mile distance to reach Alice.
Bob's speed is 6 miles per hour, so to cover the 8 miles, it will take him 8 / 6 = <<8/6=1.33>>1.33 hours.
Therefore, Bob is gaining on Alice at a rate of 8 miles in 1.33 hours, which can be simplified as approximately 6 miles per hour.
So, Bob is gaining on Alice at a speed of approximately 6 miles per hour.