P = paddling speed
C = speed of the current
Upstream: 6 = 4 (P - C)
Downstream: 6 = 3 (P + C)
4P - 4C = 6
3P + 3C = 6
12P - 12C = 18
12P + 12C = 24
Add the equations:
24P = 42
P = 42/24 = 1.75 mph
Subtract the equations:
-24C = -6
C = 0.25 mph
Hi friends!
Here is the ✨problem of the day✨
Laura and Brent paddled a canoe 6 miles upstream in four hours. The return trip took three hours. Find the rate at which Laura and Brent paddled a canoe in still water.
r= rate in still water
c=current
Rate for upstream would be the rate in still water minus the current (r-c), because the current is promoting the flow. The rate for downstream would be the rate in still water plus the current (r+c), because they are paddling against the current. Remember, distance will be the same for the return trip as well as the original downstream trip. This is a distance time rate problem, expect we are looking for rate so... (time in hours)
tr=d
Here are the equations:
4(r-c)=6 and 3(r+c)=6
SOLVE!
Here is one efficient way that I like to answer these problems.
Multiply the equation by the reciprocal of 4, which is 1/4.
Multiply the other equation by the reciprocal of 3, which is 1/3.
You then have r-c=1.5 and r+c=2.
Use the elimination method to add the two equations together.
You now have 2r=3.5
The final step is to divide by 2.
The answer is r=1.75
If you remember from earlier, time was measured in hours, so when you write your final answer in words, you will use hours. REMEMBER r REPRESENTS THE RATE IN STILL WATER!!!
You are all set to now write your final answer in words.
Sample answer: The rate in still water is 1.75 mph.
There is a chance that I got this problem wrong because I am a 5th grader who is attempting Algebra 1 Honors. Please note that it is human to err, so I might have done so. Thanks for your time!!!
♡ ♡ ♡
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