SOLUTION: Rani times herself as she kayaks 30 miles down the Derwent river with the help of the current. returning upstream against the current, she manages only 18 miles in the same amount
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Question 556173: Rani times herself as she kayaks 30 miles down the Derwent river with the help of the current. returning upstream against the current, she manages only 18 miles in the same amount of time. Rani knows that she can kayak at a rate of 12mph in still water. what is the speed of the current. Solve by setting up appropriate solution(s).
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
rate * time = distance.
when the boat and the current are going in the same direction then the rate of the current is added to the rate of the boat.
when the boat and the current are going in opposite directions then the rate of the current is subtracted from the rate of the boat.
let c = rate of the current
let b = rate of the boat.
let t = time
let d = distance.
with the current, the formula becomes:
(b+c)*t = d
against the current, the formula becomes:
(b-c)*t = d
we know the rate of the boat = 12 miles per hour.
we know the distance with the current is 30 miles.
we know the distance against the current is 18 miles.
we know the time is the same whether we are going with the current or against the current.
the formula with the current becomes:
(12+c)*t = 30
the formula against the current becomes:
(12-c)*t = 18
we need to solve both equations simultaneously to find the value of c.
we simplify both equations to get:
12*t + c*t = 30
12*t - c*t = 18
we can add both equations together and, in so doing, will eliminate the + c*t and the - c*t to get:
24*t = 48
we divide both sides of this equation by 24 to get:
t = 2
we have solved for t and the value of t is 2 hours.
we now use that value of t in either equation to solve for c.
in the first equation, we get:
12*2 + c*2 = 30 which becomes:
24 + 2*c = 30
we subtract 24 from both sides of this equation to get:
2*c = 30 - 24 = 6
we divide both sides of this equation by 2 to get:
c = 3
looks like the rate of the current is 3 miles per hour.
we substitute for c and t in the second equation to get:
12*2 - 3*2 = 18 which becomes:
24 - 6 = 18 which becomes:
18 = 18
this confirms the values for c and t are good.
they are:
t = 2
c = 3
rate of the current is 3 miles per hours.
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