Question

Swati can row her boat $5$ km/hr in still water. If it takes her one hour longer to row the boat $5.25$ km upstream than to return downstream, find the speed of the stream in km/hr.

Answer 1

Speed of the boat in still water, $b=5$ km/hr

Let speed of the stream $=s$ km/hr

Upstream speed $=b-s=5-s$

Distance travelled $=5.25$ km

Time taken, $t_1=\frac{distance}{speed}$

$t_1=\frac{5.25}{5-s}$

Downstream speed $=b+s=5+s$

Distance travelled $=5.25$ km

Time taken, $t_2=\frac{distance}{speed}$

$t_2=\frac{5.25}{5+s}$

Now,

$t_1=t_2+1$

$\frac{5.25}{5-s}=\frac{5.25}{5+s}+1$

$\frac{5.25}{5-s}-\frac{5.25}{5+s}=1$

$\frac{26.25+5.25s-26.25+5.25s}{(5-s)(5+s)}=1$

$\frac{10.5s}{25-s^2}=1$

$10.5s=25-s^2$

$s^2+10.5s-25=0$

$s^2+12.5s-2s-25=0$

$s(s+12.5)-2(s+12.5)=0$

$(s-2)(s+12.5)=0$

$s=-12.5$ or $s=2$

Speed cannot be negative. So, speed of the stream $=2$ km/hr