We have
[tex]t_1 + t+2 = \dfrac{\sqrt{s}}{4} + \dfrac{s}{1100} = .5[/tex]
Multiplying through by 1100,
[tex]275 \sqrt{s} + s = 550[/tex]
[tex]275 \sqrt{s} = 550 - s[/tex]
Squaring (which means we need to check later),
[tex]275^2 s = (550 - s)^2 = 550^2 - 1100 s + s^2[/tex]
[tex] 0 = s^2 - (1100 + 275^2) s + 550^2[/tex]
[tex]0 = s^2 - 76725 s + 302500[/tex]
[tex]s = \frac 1 2 (76725 \pm 1375 \sqrt{3113} )[/tex]
[tex]s \approx 3.94285 \textrm{ or } s \approx 76721.0571[/tex]
Clearly there's no way that giant number would work; must be extraneous.
Answer: 3.94
Merry Christmas!
