Bob was attempting to steal a chicken. When he first saw the bird, he was standing 250 yards due south of it. Both began running at the same time and ran with uniform speeds. The chicken ran due east. Instead of running northeast on a straight line, Bob ran so that at every instant he was running directly towards the chicken. Assuming that Bob ran 1 1/3 times faster than the chicken, how far did the chicken run before it was caught???
First, determine how far Bob would travel to catch the chicken if the chicken and Bob both ran forward on a straight line. Add to this the distance that Bob would travel to catch the chicken if they ran towards each other on a straight line. Divide the result by 2 and you have the distance that Bob travels. In this case, the chicken is 250 yards away, and the speeds of Bob and the chicken are in proportion of 4 to 3. So, if both ran forward on a straight line, Bob would travel 1,000 yards to overtake the chicken. If they traveled towards each other, Bob would travel four-sevenths of 250, or 142 6/7 yards. Adding the two distances and dividing by 2 gives us 571 3/7 yards for the distance traveled by Bob. Since the chicken runs at three-fourths the speed of Bob, it will have traveled three-fourths of Bob's distance, or 428 4/7 yards.