Question 1205894
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(Note to tutor @ikleyn: fix a small error in your response....)<br>
The other tutor shows a perfectly good way to set up and solve the problem.<br>
Here is a very different way to set up and solve the problem.<br>
Over some time interval, B runs 12 feet while A runs 8 feet; in that time interval  B runs 4 feet farther than A.<br>
A is 84 feet ahead of B at the start; the number of time intervals needed for B to overtake A is 84/4 = 21.<br>
So the distances the two of them run before B overtakes A are:<br>
A: 21*8 = 168 feet
B: 21*12 = 252 feet<br>
ANSWER: (distance A runs before B overtakes him) 168 feet<br>
That same solution formally....<br>
Let x be the number of time intervals in which B runs 12 feet and A runs 8 feet.<br>
12x = distance B runs
8x = distance A runs<br>
In overtaking A, B runs 84 feet farther than A:
12x = 8x+84
4x = 84
x = 21<br>
ANSWER: the distance A runs is 8x = 168 feet<br>