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

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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) About Me  (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.

D+=+r%2At

40+=+%28b-5%29%2At

40%2F%28b-5%29+=+t

t+=+40%2F%28b-5%29

It takes 40%2F%28b-5%29 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.

D+=+r%2At

40+=+%28b%2B5%29%2At

40%2F%28b%2B5%29+=+t

t+=+40%2F%28b%2B5%29

It takes 40%2F%28b%2B5%29 hours to go downstream

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Add up the two time expressions 40%2F%28b-5%29 and 40%2F%28b%2B5%29

40%2F%28b-5%29+%2B+40%2F%28b%2B5%29

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

40%2F%28b-5%29+%2B+40%2F%28b%2B5%29+=+5

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Now we solve for b.

40%2F%28b-5%29+%2B+40%2F%28b%2B5%29+=+5

40%28b%2B5%29+%2B+40%28b-5%29+=+5%28b-5%29%28b%2B5%29 Multiply both sides by the LCD %28b-5%29%28b%2B5%29 to clear out the fractions.

40%28b%2B5%29+%2B+40%28b-5%29+=+5%28b%5E2-25%29

40b%2B200+%2B+40b-200+=+5b%5E2-125

80b+=+5b%5E2-125

0+=+5b%5E2-125-80b

5b%5E2-80b-125+=+0

5%28b%5E2-16b-25%29+=+0

b%5E2-16b-25+=+0

Use the quadratic formula to get these solutions:

b=8%2Bsqrt%2889%29, b=8-sqrt%2889%29

The solutions approximate to

b=17.4339811320567, b+=+-1.4339811320566

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

The exact answer is b=8%2Bsqrt%2889%29. The approximate answer is b=17.4339811320567

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