A boat can go 5 km upstream and $$7\frac{1}{2}$$ km downstream in 45 minutes. If can also go 5 km downstream and 2.5 km upstream in 25 minutes. How much time (in minutes) will it take to go 6 km upstream?

Solution (By Examveda Team)

$$\eqalign{ & \frac{5}{{x - y}} + \frac{{15}}{{2\left( {x + y} \right)}} = \frac{3}{4}{\text{hr }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}\left( {\text{i}} \right) \cr & \frac{{2.5 \times 2}}{{x - y}} + \frac{{5 \times 2}}{{x + y}} = \frac{{5 \times 2}}{{12}}{\text{hr }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}\left( {{\text{ii}}} \right) \cr & \frac{5}{{2\left( {x + y} \right)}} = \frac{1}{{12}} \cr & x + y = 30 \cr & {\text{Put }}x + y = 30{\text{ in equation }}\left( {\text{i}} \right) \cr & \frac{5}{{x - y}} + \frac{{15}}{{2 \times 30}} = \frac{3}{4} \cr & \frac{5}{{x - y}} = \frac{1}{2} \cr & x - y = 10 \cr & {\text{Now,}} \cr & \,x + y = 30 \cr & \underline {\,x - y = 10\,} \cr & x = 20 \cr & y = 10 \cr & \frac{{6\,{\text{km}}}}{{x - y}} = \frac{6}{{10}} \times 60 = 36\min \cr} $$