SOLUTION: Lauren's boat can go 9 miles per hour in still water. How far downstream can Lauren go if the river has a current of 3 miles per hour and she must be back in 4 hours.

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Question 1191070: Lauren's boat can go 9 miles per hour in still water. How far downstream can Lauren go if the river has a current of 3 miles per hour and she must be back in 4 hours.
Found 4 solutions by josgarithmetic, ikleyn, MathTherapy, greenestamps:
Answer by josgarithmetic(39621) About Me  (Show Source):
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                   SPEEDS      TIMES       DISTANCES

downstream         9+3=12       x            12x

upstream           9-3=6        4-x           6(4-x)

TOTAL                             4

The distances both directions are equal.

12x=6%284-x%29
2x=4-x
3x=4
cross%28x=3%2F4%29
x=4%2F3

She can go cross%2812%283%2F4%29=highlight%289%29%2912%284%2F3%29=4%2A4=highlight%2816%29 miles down the river.

Answer by ikleyn(52818) About Me  (Show Source):
You can put this solution on YOUR website!
.


            The solution by @josgarithmetic is  INCORRECT,  giving incorrect answer of  9  miles.

            I came to bring a correct solution. 



                   SPEEDS      TIMES       DISTANCES

downstream         9+3=12       x            12x

upstream           9-3=6        4-x           6(4-x)

TOTAL                             4

The distances both directions are equal.

12x=6%284-x%29
2x=4-x
3x=4
x=4%2F3

She can go 12%284%2F3%29=highlight%2816%29 miles down the river.



Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!

Lauren's boat can go 9 miles per hour in still water. How far downstream can Lauren go if the river has a current of 3 miles per hour and she must be back in 4 hours.
Let distance back and forth be D
Then time Lauren will take to travel downstream is: matrix%281%2C3%2C+D%2F%289+%2B+3%29%2C+or%2C+D%2F12%29
Also, time Lauren will take to return upstream is: matrix%281%2C3%2C+D%2F%289+-+3%29%2C+or%2C+D%2F6%29
With Lauren taking 4 hours to complete round-trip, we get the following TIME equation: matrix%281%2C3%2C+D%2F12+%2B+D%2F6%2C+%22=%22%2C+4%29
D + 2D = 48 ------- Multiplying by LCD, 12
3D = 48
Distance Lauren can travel downstream and back, in 4 hours, or highlight_green%28matrix%281%2C6%2C+D%2C+%22=%22%2C+48%2F3%2C+%22=%22%2C+16%2C+miles%29%29

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Here is a solution that is quite different than shown by the other tutors.

Her downstream speed will be 9+3=12 mph; her upstream speed will be 9-3=6 mph.

Since her downstream speed is twice her upstream speed and the distances downstream and back are the same, she will spend twice as much time on the upstream trip.

Divide the 4 hours into two parts in the ratio 2:1, and you will see that she can only spend 4/3 hours on the downstream trip; she will need twice as much time -- 8/3 hours -- for the return trip.

4/3 of an hour at 12 mph takes her 16 miles.

And, while it is not needed to solve the problem, 8/3 hours at 6 mph will bring her back those same 16 miles.

ANSWER: 16 miles