Answer:
9mph
Step-by-step explanation:
Let speed of boat=x mph
Speed of current=3 mph
Upstream speed=(x-3) mph
Downstream speed =(x+3)mph
Distance=24 miles
Total time=6 hours
[tex]Time=\frac{distance}{speed}[/tex]
According to question
[tex]\frac{24}{x+3}+\frac{24}{x-3}=6[/tex]
[tex](24)\frac{x-3+x+3}{(x+3)(x-3)}=6[/tex]
[tex]2x(24)=6(x+3)(x-3)[/tex]
[tex]\frac{48x}{6}=x^2-9[/tex]
Using the identity:[tex](a+b)(a-b)=a^2-b^2[/tex]
[tex]8x=x^2-9[/tex]
[tex]x^2-8x-9=0[/tex]
[tex]x^2-9x+x-9=0[/tex]
[tex]x(x-9)+1(x-9)=0[/tex]
[tex](x-9)(x+1)=0[/tex]
[tex]x-9=0\implies x=9[/tex]
[tex]x+1=0\implies x=-1[/tex]
Speed cannot be negative
Therefore, the speed of boat=9mph
