A runner starts a race at the starting line. A second runner starts at 44 yards. If the first runner moves 7 yards each second and the second runner moves 3 yards each second, at what distance will the first runner catch the second runner?

it'll take the first runner 8 seconds.

To find out at what distance the first runner will catch the second runner, we can set up an equation.

Let's assume that the distance they will meet is "x" yards from the starting line.

Since the first runner is moving 7 yards each second and the second runner is moving 3 yards each second, we can set up the following equation:

x = 44 + 7t

Here, "t" represents the time in seconds.

We add 44 to account for the starting position of the second runner.

To solve for "t," we need to equate the distance traveled by the first runner, which is given by "x," and by the second runner, which is given by 3t (since the second runner moves 3 yards per second).

Therefore, we can set up another equation:

x = 3t

Now we can substitute the value of "x" from the first equation into the second equation:

44 + 7t = 3t

Next, we can solve for "t":

44 = 3t - 7t
44 = -4t
t = -11

Since time cannot be negative, this means that the first runner will catch the second runner at t = 11 seconds.

To find the distance at which they meet, we can substitute this value of "t" back into the first equation:

x = 44 + 7(11)
x = 44 + 77
x = 121

Therefore, the first runner will catch the second runner at a distance of 121 yards from the starting line.