SOLUTION: 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
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Question 141774This question is from textbook
: 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! This question is from textbook
You can put this solution on YOUR website! 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
