Answer
(a) River width $d=90.4 \space m$ and current speed $v_r=3.97 \space m/s$
(b) Time to cross the river $t=\frac{d}{v_{br}}=\frac{90.4}{6}=15.1 \space s$ and drift $D=3.97\times 15.1=59.95 \space m$ (downstream i.e. towards east)
Work Step by Step
(a) Speed of the boat w.r.t. ground $v_b=\sqrt{v_{br}^2-v_r^2}$
So time taken by the boat to cross the river (river width is d) $t=\frac{d}{v_b}=\frac{d}{\sqrt{v_{br}^2-v_r^2}}$
So to travel from south to north bank, $20.1=\frac{d}{\sqrt{6^2-v_r^2}}$ .....(i)
To travel from north to south bank, $11.2=\frac{d}{\sqrt{9^2-v_r^2}}$ .....(ii)
On solving equation (i) and (ii), we get
River width $d=90.4 \space m$ and current speed $v_r=3.97 \space m/s$
(b) If throttles are perpendicular to the river, then time to cross the river
$t=\frac{d}{v_{br}}=\frac{90.4}{6}=15.1 \space s$
Drift in this case, $D=v_rt=3.97\times 15.1=59.95 \space m$ (downstream i.e. towards east)
