Don uses his small motorboat to go 5 miles upstream to his f

Don uses his small motorboat to go 5 miles upstream to his favorite fishing spot. Against the current, the trip takes 5/6 hour. With the current the trip takes 1/2 hours. How fast can the boat travel in still water. What is the speed of the current?
Thanks for your help!

Solution

Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r
Let r=speed of the boat in still water
And let x=rate (speed) of the current
Going upstream we need to subtract the speed of the current: going downstream we need to add the speed of the current
Then speed upstream =r-x=5/(5/6)
5/(5/6): multiply numerator and denominator by 6/5 to get rid of the complex fraction and we get 6
So, r-x=6--------------------------------------eq1
And speed downstream=r+x=5/(1/2)=10
and r+x=10------------------------------------eq2
add eq1 and eq2
2r=16 divide both sides by 2
r=8 mph-----------------------------speed of boat in still water
substitute r=8 into eq1
8-x=6 subtract 8 from each side
8-8-x=6-8 collect like terms
-x=-2 divide each side by -1
x=2 mph------------------------------speed of current
CK
5 =6*(5/6)
5=5
and
5=10*(1/2)
5=5

Hope this help