SOLUTION: Hello! I could use some help with this word problem. To celebrate Lewis and Clark expedition, you are traveling 40 miles upstream and then 40 miles downstream in a canoe. The s

Question 919232: Hello! I could use some help with this word problem.
To celebrate Lewis and Clark expedition, you are traveling 40 miles upstream and then 40 miles downstream in a canoe. The speed of the river current is 5 miles an hour. If the trip takes you 5 hours, how fast do you travel if the river has no current?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let b = speed of boat in mph

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Upstream: You go slower since you are going against the current. The actual speed is b-5. The "-5" is due to the 5 mph current slowing you down.

It takes hours to go upstream

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Upstream: You go faster since you are going with the current. The actual speed is b+5. The "+5" is due to the 5 mph current speeding you up.

It takes hours to go downstream

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Add up the two time expressions and

Set this sum equal to 5 because the two time values must add to 5 hours. This is the total round trip time.

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Now we solve for b.

Multiply both sides by the LCD to clear out the fractions.

Use the quadratic formula to get these solutions:

,

The solutions approximate to

,

Toss out the negative answer because a negative speed makes no sense in this case.

The exact answer is . The approximate answer is

Let me know if you need more help or if you need me to explain a step in more detail.
Feel free to email me at jim_thompson5910@hotmail.com
or you can visit my website here: http://www.freewebs.com/jimthompson5910/home.html

Thanks,

Jim
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