Jan, John went 6 mi upstream against 2 mph current....

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candy5171

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I need help with the following word problem. I have done similar word problems with no problems, but have spent hours and hours on this one...I know that the answer is 4 miles per hour because the answers are provided in the back of the book, but I keep getting 3 miles per hour. Please show me the formula you create to get the correct answer. Thank you soooo much!!

Jan and John took a canoeing trip, traveling 6 miles upstream againsta a 2 mile/hour current. They then returned to the same point downstream. If their entire trip took 4 hours, how fast can they paddle in still water? [Hint: If r is their rate (in miles per hour) in still water, their rate upstream is r-2 and their rate downstream is r+2.]
 
candy5171 said:
I need help with the following word problem. I have done similar word problems with no problems, but have spent hours and hours on this one...I know that the answer is 4 miles per hour because the answers are provided in the back of the book, but I keep getting 3 miles per hour. Please show me the formula you create to get the correct answer. Thank you soooo much!!

Jan and John took a canoeing trip, traveling 6 miles upstream againsta a 2 mile/hour current. They then returned to the same point downstream. If their entire trip took 4 hours, how fast can they paddle in still water? [Hint: If r is their rate (in miles per hour) in still water, their rate upstream is r-2 and their rate downstream is r+2.]
Click to expand...

Please show us your work - even if you know it is wrong - so that we know where to begin to help you.
 
Distance = Rate x Time
Time = Distance / Rate
Time = 4 hours

Distance Rate Time
Upstrm 6 (r – 2) 6 ÷ (r – 2)
Dwnstrm 6 (r + 2) 6 ÷ (r + 2)

(6 ÷ (r – 2)) + (6 ÷ (r + 2)) = 4 LCD is (r – 2)(r + 2)

multiply both sides by LCD
(6 ÷ (r – 2)) x ((r + 2)(r – 2)) + (6 ÷ (r + 2)) x ((r + 2) (r - 2)) = 4 (r - 2) (r + 2)

cross-cancel
6r + 12 + 6r -12 = 4 (r - 2) (r + 2)

combine like terms
12r = 4 (r - 2) (r + 2)

Divide both sides by 4
3r = (r - 2)(r + 2)

3r = r[sup:uhc5z3io]2[/sup:uhc5z3io] + 2r - 2r -4

3r = r[sup:uhc5z3io]2[/sup:uhc5z3io] - 4

this is where i get stuck!!!
 
candy5171 said:
...Divide both sides by 4
3r = (r - 2)(r + 2)

3r = r[sup:2eyjsedb]2[/sup:2eyjsedb] + 2r - 2r -4

3r = r[sup:2eyjsedb]2[/sup:2eyjsedb] - 4

You are soooo close

\(\displaystyle r^2\, - \, 3r \, - 4 \, = \, 0\)

above is a quadratic equation. One good way to solve this, is to factorize the Left-Hand-Side.

\(\displaystyle (r\, - \, 4)\cdot (r \, + \, 1) \, = \, 0\)

Can you continue from here and solve for 'r'?
Click to expand...
 
Thank you so much!! \

r=4 or r=-1

only 4 works!!

You rock!! You made my weekend!!
 
Re: Word Problem-HELP!!

Check your answer to make sure it works.

How long did it take to go up the stream? --- t[sub:fh4jei4m]1[/sub:fh4jei4m]

How long did it take to go down stream?--- t[sub:fh4jei4m]2[/sub:fh4jei4m]

How long was the total trip? --- t[sub:fh4jei4m]1[/sub:fh4jei4m] + t[sub:fh4jei4m]2[/sub:fh4jei4m]

Does it match the given data (4 hrs)?
 
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