SOLUTION: How far upstream can a motorboat travel at 8 mi/hr and still return downstream at 12 mi/hr in a total time of 4 hr?

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Question 263749: How far upstream can a motorboat travel at 8 mi/hr and still return downstream at 12 mi/hr in a total time of 4 hr?

Found 5 solutions by mananth, jsmallt9, ikleyn, josgarithmetic, MathTherapy:
Answer by mananth(16949)   (Show Source):
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How far upstream can a motorboat travel at 8 mi/hr and still return downstream at 12 mi/hr in a total time of 4 hr?
let the time taken upstream be x
the down stream time will be 4-x hrs.
speed upstream = 8mph
distance upstream = 8*x
distance down stream = 12*(4-x)
8x= 48-12x
16x=48
x=3 hour---------------------------------- 24 miles
down stream time = 1hour

Answer by jsmallt9(3759)   (Show Source):
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There is an error in a solution provided by another tutor. The other solution is correct up to
8x = 48 - 12x
Next we add 12x to each side:
20x = 48 (NOT 16x)
Dividing by 20 we get:
x = 48/20 = 12/5
Since x is the amount of time spent traveling upstream it is not the answer to the question. How far you can travel upstream is miles.

Answer by ikleyn(53742)   (Show Source):
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.
How far upstream can a motorboat travel at 8 mi/hr and still return downstream at 12 mi/hr in a total time of 4 hr?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

        The solution in the post by @mananth is INCORRECT due to arithmetic error.
        His answer "3 hours upstream and 1 hour downstream" does not work, as everybody can check manually.
        I came to bring a correct solution.

let the time taken upstream be x
the down stream time will be 4-x hrs.
speed upstream = 8 mph
distance upstream = 8*x
distance downstream = 12*(4-x)
8x = 48-12x
20x = 48
x = 48/20 = 2.4 hours = 2 hours and 24 minutes ---------------------------------- 24 miles
downstream time = 4 hours - 2.4 hours = 1.6 hours = 1 hour and 36 minutes.

The one way distance is 2.4 hours upstream * 8 mph = 19.2 miles.

ANSWER. How far is 19.2 miles.

Solved correctly.

Answer by josgarithmetic(39790)   (Show Source):
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Upstream and then downstream
8 and 12 miles per hour
Total time 4 hours.

If t hours going at 12 mph then 4-t going at 8 mph.

distance

Answer by MathTherapy(10801)   (Show Source):
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How far upstream can a motorboat travel at 8 mi/hr and still return downstream at 12 mi/hr in a total time of 4 hr? ********************************* Let distance, back and forth, be D Then time taken to travel upstream, is Also, time taken to travel downstream, is We then get the following TOTAL-TIME equation: 3D + 2D = 96 ---- Multiplying by LCD, 24 5D = 96 Distance, back and forth, or