Because they're consecutive, it means that the first one is x, the second one is x+1, the third one is x+2 (x+1+1), and the fourth one is x+3. Because we're given that the sum of all of them is 682, just add all of them together:
x+(x+1)+(x+2)+(x+3)=682
x+x+x+x+1+2+3=682
4x+6=682
4x+6-6=682-6
4x=676
x=676/4
x=169
Thus, the consecutive integers are: 169, 170, 171, 172
X = t - 3 is also -t = -x - 3 or t=x+3
Substitute it in
y=2/t+5
y=2/(x+3)+5
Let y=0 to solve for x
0=2/(x+3)+5
-5= 2/(x+3)
-10=x+3
-7=x
Now solve for t
t = x+3
t = (-7)+3
t = -4
Now we can solve for y
y = 2/(-4)+5
y = -0.5+5
y = 4.5
To check
4.5 = 2/(-4) + 5
4.5 = -0.5 + 5
4.5 = 4.5
-7 = -4 - 3
-7 = -7
Therefore
x = -7
y = 4.5
t = -4
