Question 177648: Joann took 20 miuntes to drive her boat upstream to water-ski at her favorite spot. Coming back later in the day, at the same boat speed, took her 15 minutes. If the current in that part of the river is 5 km per hr, what was her boat speed?
Answer by gonzo(654)   (Show Source):
You can put this solution on YOUR website! equation you are looking for is rate * time = distance.
going upstream she is working against the current (combined rate = boat minus current)
coming downstream she is working with the current (combined rate = boat plus current).
let x = the rate of the boat.
let d = the distance.
going upstream:
(x-5)*20 = d
coming downstream:
(x+5)*15 = d
since both equations equal d, then they are equal to each other, so:
(x-5)*20 = (x+5)*15
expanding, this becomes:
20*x - 100 = 15*x + 75
subtract 15*x from both sides and add 100 to both sides to get:
20*x - 15*x = 75 + 100
which becomes:
5*x = 175
divide both sides by 5 to get:
x = 35 miles per hour
this means that the boat's speed is 35 miles per hour.
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to prove this is correct, substitute in the original equation of:
(x-5)*20 = (x+5)*15
which becomes:
(35-5)*20 = (35+5)*15
which becomes:
30*20 = 40*15
divide both sides by 15 to get:
30/15*20 = 40
which becomes:
2*20 = 40
which is true so the values for the boat speed are good.
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your answer is:
speed of the boat is 35 miles per hour.
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