Question

State the following statement is True or False

A crew can row a certain course up stream in $58.5$ minutes, they can row the same course down stream in $10$ minutes less than they could row it in still water. Therefore it takes 56 min to reach downstream

• A. True
• B. False

Answer 1

The correct option is B False

Let the distance be $x$

and speed of course $=V$

speed of steam $=U$

Upstream $=58.5=\frac{x}{V-U}$

Downstream $\left(t_1\right)=\frac{x}{V+U}$
In still water $t=\frac{x}{V}$

$10=t-t_1=\frac{x}{V}-\frac{x}{V+U}10=\frac{x(V+U-V)}{V(V+U)}=\frac{Ux}{V(V+U)}10=\frac{U}{V}\frac{\left(58.5\right)(V-U)}{(V+U)}10V^2+10UV=58.5UV-58.5U^{2}10V^2-48.5UV+58.5U^2=0V=\frac{+48.5U\pm \sqrt{({\left(48.5\right)}^2-4\times 10\times 58.5)U^2}}{20}V=\frac{48.5U\pm 3.5U}{20}V=2.6U,2.25Ux=\frac{10V(V+U)}{U}=93.6U,73.128U{t}_{down}=\frac{x}{V+U}=26min,22.5min$

Hence, the statement is false.