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

In summary, the conversation involves planning a three-day canoe trip on the Roaring Fork River and determining the start time on the third day to meet their friend. To solve the problem, the speed of the current is defined as $c$ and the rates and time for traveling upstream and downstream are calculated in terms of $c$. It is determined that it will take 7 hours to travel the same distance downstream and the start time is 10 am to meet their friend at 5 pm.
  • #1
paulmdrdo1
385
0
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.?
 
Mathematics news on Phys.org
  • #2
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?
 
  • #3
2c-c = their rate upstream
2c+c = their rate downstream

are these correct?
 
  • #4
Yes, although you can simplify them...
 
  • #5
c = rate upstream
3c = rate downstream

what's next?

21c = distance traveled

21c=3c(t)

t = 7 hours

how do I determine the time?
 
  • #6
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?
 
  • #7
It's 10 pm
 
  • #8
Well, it's actually 10 am. :D
 

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

1. What is a distance - linear equation?

A distance - linear equation is a mathematical representation of the relationship between distance and a corresponding linear function. It is used to calculate the distance between two points on a graph, or to determine the slope of a straight line.

2. How do you calculate the distance between two points using a linear equation?

To calculate the distance between two points using a linear equation, you can use the distance formula: d = √[(x2 - x1)^2 + (y2 - y1)^2], where (x1, y1) and (x2, y2) represent the coordinates of the two points on the graph.

3. What is the slope-intercept form of a distance - linear equation?

The slope-intercept form of a distance - linear equation is y = mx + b, where m represents the slope of the line and b represents the y-intercept (the point where the line crosses the y-axis).

4. How do you graph a distance - linear equation?

To graph a distance - linear equation, you can plot the y-intercept (b) on the y-axis, and then use the slope (m) to find additional points on the line. You can also use the slope-intercept form to identify the rise (change in y) and run (change in x) of the line.

5. What are some real-life applications of distance - linear equations?

Distance - linear equations are used in many different fields, such as physics, engineering, and economics. They can be used to calculate the speed of an object, determine the trajectory of a projectile, or analyze the relationship between cost and production in a business setting.

Hot Threads

Recent Insights

Back
Top