A family is canoeing downstream (with the current). Their speed relative to the banks of the river averages $2.75 mi / h$. During the return trip, they paddle upstream (against the current), averaging 1.5 milh relative to the riverbank. Write and solve a system of equations to find the family's paddling speed in still water. Let $s$ equal the families paddling speed and $c$ represent the current.
a. $\quad s + c =2.75$
$s-c=1.5$
$2.125 mi / h$
b. $\quad 2.75 s= c$
$1.5 s=c$
$1.725 mi / h$
c. $s + c =2.75$
$c-s=1.5$
$.60 mi / h$
d. $\quad 2.75 c = s$
$1.5 c=s$
$30 mi / h$
Please select the best answer from the choices provided
Answer (2)
Set up a system of equations: s + c = 2.75 and s − c = 1.5 , where s is the paddling speed and c is the current speed.
Add the two equations to eliminate c : 2 s = 4.25 .
Solve for s : s = 2 4.25 = 2.125 .
The family's paddling speed in still water is 2.125 mi / h .
Explanation
Problem Analysis Let's analyze the problem. We are given the speed of a canoe going downstream and upstream. We need to find the speed of the canoe in still water. Let s be the speed of the canoe in still water and c be the speed of the current. When going downstream, the speed of the canoe is the sum of its speed in still water and the speed of the current, so s + c = 2.75 . When going upstream, the speed of the canoe is the difference between its speed in still water and the speed of the current, so s − c = 1.5 . We have a system of two equations with two variables:
System of Equations The system of equations is: s + c = 2.75 s − c = 1.5
Elimination Method We can solve this system by adding the two equations to eliminate c :
( s + c ) + ( s − c ) = 2.75 + 1.5 2 s = 4.25
Solving for s Now, we can solve for s :
s = 2 4.25 = 2.125
Solving for c Now we can find the current c by substituting the value of s into one of the equations. Let's use the first equation: 2.125 + c = 2.75 c = 2.75 − 2.125 = 0.625
Final Answer The family's paddling speed in still water is 2.125 mi/h. The correct answer is A.
Examples
Imagine you're rowing a boat in a river. When you row with the current, your speed increases, and when you row against the current, your speed decreases. This problem helps you understand how to calculate your speed in still water and the speed of the current by using a system of equations. This concept is useful in various real-life situations, such as planning travel routes, understanding fluid dynamics, or even optimizing the performance of machines in moving fluids.
The family's paddling speed in still water is determined to be 2.125 mi/h by setting up a system of equations based on their speeds downstream and upstream. The correct answer is option A: 2.125 mi/h.
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