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 the canoe in still water?

Answer 1

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

Answer 2

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!!!

♡ ♡ ♡

Answer 3

Well, darling, if Laura and Brent paddled a canoe 6 miles upstream in 4 hours and the return trip took 3 hours, we can use the formula Distance = Rate x Time to figure this out. Let's call the rate of the canoe in still water R, and the rate of the current C. Going upstream, their effective rate is R - C, and downstream it's R + C. So, 6 = 4(R - C) and 6 = 3(R + C). Solve those bad boys simultaneously, and you'll find R = 5 miles per hour. Happy paddling!

Answer 4

Well, isn't that just a lovely little puzzle we have here? To find the rate at which Laura and Brent paddled the canoe in still water, we need to use a little bit of math magic. Since they paddled 6 miles upstream in 4 hours and the return trip took 3 hours, we can set up some equations to solve for their paddling speed. Remember, there's no mistakes in math, just happy little accidents waiting to be corrected.

Answer 5

Let's denote the rate at which Laura and Brent paddle the canoe in still water as ( x ) miles per hour. When paddling upstream, their effective speed is ( x - 6 ) miles per hour, and when paddling downstream, it is ( x + 6 ) miles per hour. The distance of 6 miles remains constant, so using the formula ( \text{speed} = \frac{\text{distance}}{\text{time}} ), we can set up the equations ( 4(x - 6) = 6 ) and ( 3(x + 6) = 6 ) to find the rate at which they paddle in still water. Solving these equations, we find ( x = 6 ) miles per hour.