Answer
$11\frac{ft}{sec}$
Work Step by Step
The given balloon is rising: $\frac{dy}{dt}=1\frac{ft}{sec}$
bicycle speed: $\frac{dx}{dt}=17\frac{ft}{sec}$
at $t=3sec$
balloon rising $y=68 ft $ high
bicycle moved $x=51ft$
on applying the Pythagorean Theorem:
$s^2=x^2+y^2$
$s=\sqrt{(68^2+51^2)}=85 ft$
on differentiating with respect to time:
$2s\frac{ds}{dt}=2x\frac{dx}{dt}+2y\frac{dy}{dt}$
$\frac{ds}{dt}=\frac{1}{s}(x\frac{dx}{dt}+y\frac{dy}{dt})$
$\frac{ds}{dt}=\frac{1}{85}(51(17)+68(1))=11\frac{ft}{sec}$
Thus the final answer is: $11\frac{ft}{sec}$