How Long Should Milo and Bernard Paddle Downstream to Meet Vince by 5 P.M.?

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Discussion Overview

The discussion revolves around a problem involving Milo and Bernard's canoe trip on the Roaring Fork River, specifically calculating the time they need to start paddling downstream to meet their friend Vince at a designated time. The focus includes understanding their paddling rates relative to the river current and determining the timing of their journey over three days.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant requests assistance in solving the problem, indicating a need for guidance on how to start.
  • Another participant suggests defining the speed of the current as $c$ and asks how to express their upstream and downstream speeds in terms of $c$.
  • A participant proposes the equations for their rates: $2c - c$ for upstream and $2c + c$ for downstream, seeking confirmation of their correctness.
  • There is agreement on the rates, with a simplification to $c$ for upstream and $3c$ for downstream being suggested.
  • A calculation of total distance traveled upstream over 21 hours is presented, leading to a time calculation for the downstream journey.
  • Another participant notes that since they travel three times faster downstream, it will take one-third of the time to cover the same distance.
  • Participants discuss the timing of their departure, with one suggesting that 7 hours before 5 PM is 10 PM, while another corrects this to 10 AM.

Areas of Agreement / Disagreement

There is some confusion regarding the timing of their departure, with differing opinions on whether it is 10 PM or 10 AM. The discussion does not reach a consensus on the final answer.

Contextual Notes

Assumptions about the relationship between paddling rates and the current speed are present, but not fully resolved. The discussion includes various mathematical steps that may depend on additional clarifications or definitions.

paulmdrdo1
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please I need assistance with this problem

help me get started

Roughing It Milo and Bernard are planning a three-day canoe trip
on the Roaring Fork River. Their friend Vince will drop them off at
the Highway 14 bridge. From there they will paddle upstream for
12 hours on the first day and 9 hours on the second day. They have
been on this river before and know that their average paddling rate
is twice the rate of the current in the river. At what time will they
have to start heading downstream on the third day to meet Vince at
the Highway 14 bridge at 5 P.M.?
 
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I would begin by defining $c$ as the speed of the current. So, how fast will they move upstream and how fast will they move downstream in terms of $c$? If it takes them 9 + 12 = 21 hours to travel upstream, then how long will it take to travel this same distance downstream?
 
2c-c = their rate upstream
2c+c = their rate downstream

are these correct?
 
Yes, although you can simplify them...
 
c = rate upstream
3c = rate downstream

what's next?

21c = distance traveled

21c=3c(t)

t = 7 hours

how do I determine the time?
 
Good, since they travel 3 times as fast downstream as upstream it will take them 1/3 as long to travel the distance.

What time is 7 hours before 5 pm?
 
It's 10 pm
 
Well, it's actually 10 am. :D