Answer: Speed of the current is 3 miles per hour.
Step-by-step explanation:
Since we have given that
Speed of motor boat = 12 miles per hour
Distance traveled upstream = 45 miles
Let the speed of the current be x
Total time taken by upstream and downstream = 8 hours
Relative speed for downstream is given by
[tex]12+x[/tex]
Relative speed for upstream is given by
[tex]12-x[/tex]
According to question, we have
[tex]\frac{45}{12+x}+\frac{45}{12-x}=8\\\\\frac{45(12-x)+45(12+x)}{(12-x)(12+x)}=8\\\\\frac{45(12-x+12+x)}{144-x^2}=8\\\\\frac{24}{144-x^2}=\frac{8}{45}\\\\45\times 24=8(144-x^2)\\\\45\times 3=144-x^2\\\\135=144-x^2\\\\135-144=-x^2\\\\-9=-x^2\\\\x=\sqrt{9}=\pm3\\\\\text{But x=-3 will be igonored as speed cant be in negative}\\\\x=3\ mile\ per\ hour[/tex]
Hence, Speed of the current is 3 miles per hour.
