Answer :
Given:
Speed in still water = 12 miles per hour
Distance travel in upstream = 45 miles
Distance travel in downstream = 45 miles
Total time = 8 hours
To find:
The speed of current.
Solution:
Let the speed of current be x miles per hour.
Speed in upstream = (12-x) miles per hour
Speed in downstream = (12+x) miles per hour
We know that,
[tex]Time=\dfrac{Distance }{Speed}[/tex]
Time to cover 45 miles in upstream = [tex]\dfrac{45}{12-x}[/tex]
Time to cover 45 miles in downstream = [tex]\dfrac{45}{12+x}[/tex]
Total time is 8 hours. So,
[tex]\dfrac{45}{12-x}+\dfrac{45}{12+x}=8[/tex]
[tex]45\left (\dfrac{1}{12-x}+\dfrac{1}{12+x}\right)=8[/tex]
Taking LCM, we get
[tex]45\left (\dfrac{12+x+12-x}{12^2-x^2}\right)=8[/tex]
[tex]45\left (\dfrac{24}{144-x^2}\right)=8[/tex]
[tex]\dfrac{45\times 24}{8}=144-x^2[/tex]
On further simplification, we get
[tex]45\times 3=144-x^2[/tex]
[tex]135=144-x^2[/tex]
[tex]x^2=144-135[/tex]
[tex]x^2=9[/tex]
Taking square root on both sides.
[tex]x=\pm \sqrt{9}[/tex]
[tex]x=\pm 3[/tex]
Speed cannot be negative. So, x=3 only.
Therefore, the speed of the current is 3 miles per hour.