SOLUTION: Jane took 30 min 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 min. If the cu

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Question 1107789: Jane took 30 min 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 min. If the current in that part of the river is 6 km per​ hr, what was her boat speed in still​ water?
Found 4 solutions by mananth, ikleyn, timofer, greenestamps:
Answer by mananth(16949) About Me  (Show Source):
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Jane took 30 min 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 min. If the current in that part of the river is 6 km per​ hr, what was her boat speed in still​ water?
Let boat speed in still water be x
current speed = 6km/h
Let distance be y km
upstream speed = (x-6) km/h.
downstream speed = (x+6) km/h
time = distance / speed
y/(x-6) =1/2 hour
2y= x-6.............1
y/(x+6) = 1/4 hour
4y = x+6...............2
multiply equation (1) by 2
we get
4y= 2x-12...............3
therefore equation (2) = (3)
x+6 = 2x-12
2x-x = 18
x= 18
Speed of boat in still water is 18kmh




Answer by ikleyn(53619) About Me  (Show Source):
You can put this solution on YOUR website!
.
Jane took 30 min 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 min.
If the current in that part of the river is 6 km per hr, what was her boat speed in still water?
~~~~~~~~~~~~~~~~~~~~~ 


Let boat speed in still water be x
The speed of the current = 6 km/h

upstream speed = (x-6) km/h.
downstream speed = (x+6) km/h


distance = time * speed


Distance upstream is  1/2 of an hour * (x-6) km/h

    d = %281%2F2%29%2A%28x-6%29 kilometers.


Distance downstream is  1/4 of an hour * (x+6) km/h

    d = %281%2F4%29%2A%28x%2B6%29 kilometers.


The distance is the same in both directions - - - so, we have this equation 

    %281%2F2%29%2A%28x-6%29 = %281%2F4%29%2A%28x%2B6%29     (1)


Multiply equation (1) by 4  (both sides).  We get

    2(x-6) = x + 6,

    2x - 12 = x + 6,

    2x - x = 12 + 6,

       x   =    18.


ANSWER.  The speed of boat in still water is 18 km/h.



Answer by timofer(144) About Me  (Show Source):
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Same distance each way.
If b is for the boat speed when no current, then
upstream distance %28b-6%29%281%2F2%29
downstream, same distance %28b%2B6%29%281%2F4%29

%28b-6%29%2F2=%28b%2B6%29%2F4
2%28b-6%29=b%2B6
2b-12=b%2B6
b=6%2B12
b=18-----------------------------speed of boat without a current

Answer by greenestamps(13296) About Me  (Show Source):
You can put this solution on YOUR website!


The responses from the other tutors show solutions using an equation that says the distances the two directions are the same.

A different setup makes the algebra needed to solve the problem easier.

Since the distances are the same and the time returning is half the time going, the speed returning is twice the speed going.

Let the boat speed by x; then the speed going is x-6 and the speed returning is x+6:

x%2B6=2%28x-6%29
x%2B6=2x-12
18=x

ANSWER: 18 km/hr