A boat traveled downstream a distance of 80 mi and then came right back. If the speed of the current was 7 mph and the total trip took 3 hours and 20 minutes, find the average speed of the boat relative to the water.

Answers

Answer 1

recall your d = rt, distance = rate * time.

going forth and back is 80 miles, thus upstream as well as downstream is just 80 miles.

now, bear in mind that say, the boat has a "still water" of "b", when going downstream, is not going "b" fast is going "b+7" because the current's is adding to it, likewise when is going upstream is going "b-7" because is going against the current and thus the current is eroding speed from it.

now, the whole trip took 3 hours and 20 minutes, bearing in mind that 20 minutes is 1/3 of an hour, so is 3 and 1/3 hours, or 10/3 of hours.

if say it took "t" hours going down, then going up it took the slack from 10/3 and "t", that is, it took "10/3 - t".

[tex]\bf \begin{array}{lccclll} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ &------&------&------\\ Downstream&80&b+7&t\\ Upstream&80&b-7&\frac{10}{3}-t \end{array} \\\\\\ \begin{cases} 80=t(b+7)\implies \frac{80}{b+7}=\boxed{t}\\\\ 80=(b-7)\left(\frac{10}{3}-t \right)\\ ----------\\ 80=(b-7)\left(\cfrac{10}{3}- \boxed{\frac{80}{b+7}} \right) \end{cases}[/tex]

[tex]\bf \cfrac{80}{b-7}=\cfrac{10}{3}-\cfrac{80}{b+7}\implies \cfrac{80}{b-7}=\cfrac{10(b+7)-80(3)}{3(b+7)} \\\\\\ \cfrac{80}{b-7}=\cfrac{10b+70-240}{3(b+7)}\implies \cfrac{80}{b-7}=\cfrac{10b-170}{3(b+7)} \\\\\\ 3(b+7)80=(b-7)(10b-170)\\\\\\ 240(b+7)=(b-7)(10b-170) \\\\\\ 240b+1680=10b^2-240b+1190\implies 0=10b^2-480b-490 \\\\\\ 0=b^2-480b-49\implies 0=(b-49)(b+1)\implies b= \begin{cases} \boxed{49}\\ -1 \end{cases}[/tex]

Answer 2

Final answer:

By converting the total trip time to minutes, using the formula for speed (distance/time), and using a system of equations representing the total trip speed when the boat is moving downstream and upstream, we can find the average speed of the boat relative to the water.

Explanation:

To solve this problem, we first need to convert the total trip time to minutes to make calculations easier. Given in the problem, 3 hours 20 minutes equates to 200 minutes. Next, we should use the formula for speed, which is distance divided by time. We know that the total distance traveled by the boat is 80 miles downstream and 80 miles back, totaling 160 miles.

When moving downstream, the speed of the boat and the speed of the current both aid in the boat’s motion. Thus we have speed of the boat = speed of the boat in still water + speed of the current. However, when the boat is moving upstream, the speed of the current works against the boat's motion. Thus we have speed of the boat = speed of the boat in still water - speed of the current.

By using the system of these equations and the fact that total time equals total distance divided by the speed of the boat, we can find the speed of the boat in still water, which represents the average speed of the boat relative to the water.

Learn more about Average Speed Calculation here:

https://brainly.com/question/680492

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Related Questions

The campsite shop sells boxes of Funshine Cereal.

The base of each box is a 180 mm x 60 mm rectangle.

The shelf where the boxes are displayed is a 65 cm x 35 cm rectangle.
Work out the maximum number of boxes that will fit on the shelf.

Answers

there are 10 mm in 1 cm, so 180 mm is really just 18cm and 60 mm is just 6cm.

so how much area each box's base takes up? 18x6 centimeters, or 108cm.

the shelf is a 65x35 so is 2275 centimeters in available area.

how many times does 108 go into 2275? well, 2275/108, that many would fit in the shelf

Answer:D 3,888

Step-by-step explanation:

Which two fixed points define the shape of a hyperbola?

A.) center and focus
B.) focus and directrix
C.) two foci
D.) vertex and focus

Answers

C). The two foci points determine the shape of the hyperbola.

C is the answer learned this last year

Segment MN has endpoints at M(2,5) and N(-4,3). What is the midpoint of the segment?

Answers

Final answer:

To find the midpoint of segment MN, we can use the midpoint formula which states that the coordinates of the midpoint are the average of the x-coordinates and the average of the y-coordinates of the endpoints. Using this formula, we find that the midpoint of segment MN is (-1, 4).

Explanation:

To find the midpoint of the segment MN, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint are the average of the x-coordinates and the average of the y-coordinates of the endpoints.

Let's calculate the x-coordinate of the midpoint:

x-coordinate = (x1 + x2) / 2 = (2 + (-4)) / 2 = -2 / 2 = -1.

Now, let's calculate the y-coordinate of the midpoint:

y-coordinate = (y1 + y2) / 2 = (5 + 3) / 2 = 8 / 2 = 4.

Therefore, the midpoint of segment MN is (-1, 4).

Final answer:

The midpoint of the segment MN with endpoints M(2,5) and N(-4,3) is (-1, 4).

Explanation:

To find the midpoint of a segment, we can use the midpoint formula. The midpoint formula states that the x-coordinate of the midpoint is the average of the x-coordinates of the endpoints, and the y-coordinate of the midpoint is the average of the y-coordinates of the endpoints.

For segment MN with endpoints M(2,5) and N(-4,3), we can calculate the x-coordinate of the midpoint by averaging the x-coordinates:

(2 + (-4)) / 2 = -1

And we can calculate the y-coordinate of the midpoint by averaging the y-coordinates:

(5 + 3) / 2 = 4

Therefore, the midpoint of segment MN is (-1, 4).

18+27 write the sum of the numbers as the product of their GCF and another sum

Answers

ghhfbdnxndnxnxnxxnxnxnbxbzbzbbxbx

what is the height of a box with a volume of 50 cubic meters, length of 10 meters, and which of 2 meters

Answers

h = v over l (w)
so 50 divided by 20
= 2.5

the answer is 2.5 alright

least common multiple of 17,3,7

Answers

Least common multiple is 357.

A passenger plane left Rome and flew toward Jakarta. one hour later a cargo plane left flying 26 km/h faster in an effort to catch up to it. After 11 hours the cargo plane finally caught up. find the passenger plane's average speed.

Answers

The first plane would be going about 23.83 km/h

What is 8.478 in expanded form

Answers

8 ones 4 tenths 7 hundredths and 8 thousandths

Based on the empirical rule, what percent of the observations will lie between plus or minus two standard deviations from the mean

Answers

Empirical rule for asymmetrical, chime formed recurrence conveyance, around 68% of the perceptions will exist in addition to and short one standard deviation of the mean; around 95% of the perceptions will exist in addition to and less two standard deviations of the mean; and for all intents and purposes every one of the (99.7%) will exist in addition to and less three standard deviations of the mean.

Find all real zeros of the function y=-9x-1

Answers

For zeros of the function (y is the function, a function of x) we need y = 0 so that in turn means we need - 9x - 1 = 0 or - 9x = 1 (i.e. add 1 to both sides); now divide by - 9, and x = 1/-9 which is exactly the same as - 1/9 or - (1/9) and this is the only zero of the function.

or

If y = -9x - 1,

When y = 0
0 = -9x - 1
0 + 1 = -9x - 1 + 1
1 = -9x
1/9 = -9x/9
1/9 = -x
1/[9 X (-1)] = -x/-1
- (1/9) = x

When x = 0
y = (-9 X 0) - 1
y = 0 - 1
y = - 1

Answer:

B.- 1/9

Step-by-step explanation:

twelve times the sum of a number and 2 is equal to 36. what is the number

Answers

12(x+2)=36
12x+24=36
12x=12
x=1

12(x+2)=36
12x+24=36
-24. -24
12x=12
/12. /12
x=1

What property justifies 4-37-25=4-25-37

Answers

the commutative property

3-i/1+i please answer in a +bi form

Answers

now... let's multiply the denominator and numerator by the conjugate of the denominator as already suggested, which is just the same, but with a different sign in the middle, 1 - i.

[tex]\bf \textit{difference of squares} \\ \quad \\ (a-b)(a+b) = a^2-b^2\qquad \qquad a^2-b^2 = (a-b)(a+b) \\\\\\ \textit{also recall that }\qquad i^2=(\sqrt{-1})(\sqrt{-1})\implies i^2=-1\\\\ -------------------------------\\\\[/tex]

[tex]\bf \cfrac{3-i}{1+i}\cdot \cfrac{1-i}{1-i}\implies \cfrac{(3-i)(1-i)}{(1+i)(1-i)}\implies \cfrac{(3-i)(1-i)}{(1^2)-(i^2)} \\\\\\ \cfrac{3-3i-i+i^2}{1^2-(-1)}\implies \cfrac{3-3i-i+(-1)}{1+1}\implies \cfrac{3-1-3i-i}{2} \\\\\\ \cfrac{2-4i}{2}\implies \cfrac{\underline{2}(1-2i)}{\underline{2}}\implies 1-2i[/tex]

Cindy was asked by her teacher to subtract 3 from a certain number and then divide the result by 6. Instead, she subtracted 6 and then divided the result by 3, giving an answer of 35. What would her answer have been is she had worked the problem correctly?

Answers

she subtracted 6 from a certain number and then divided the result by 3, giving her 35.

(x - 6) / 3 = 35
x - 6 = 35*3
x - 6 = 105
x = 105 + 6
x = 111

so she should have subtracted 3, then divided by 6
(111 - 3) / 6 = 108/6 = 18 <===

Taking the answer 35 multiplying it by 3 and adding 6 would give the original number chosen.
(35 × 3) - 6 = 111
Original number chosen is 111.
Now perform the correct operations.
111 - 3 = 108
108 ÷ 6 = 18
The correct answer is 18

Hope it helped!

is the number /2500 rational or irrational? explain

Answers

2500 is rational, because it can be turned into a fraction. A rational number is a number that can be written as a ratio. That means it can be written as a fraction, in which both the numerator (the number on top) and the denominator (the number on the bottom) are whole numbers. While a irrational number can be written as a decimal, but not as a fraction, and has endless non-repeating digits to the right of the decimal point.
Ex of rational: The number 8 is a rational number because it can be written as the fraction 8/1.
Ex of irrational: π = 3.141592…
Hoped it helped! :)

Answer:

Rational

Step-by-step explanation:

If you ask about number "2500" then it is rational since 2500 can be changed in the form of p/q, where q ≠ 0. Like, 2500, 5000/2 or so on.

and if you ask about "[tex]\frac{number}{2500}[/tex]" then it is also rational and it is terminating rational number because denominator (2500) can be converted in [tex]2^{m} *5^{n}[/tex].

a circle is centered at the point -3,2) and passes through the point (1,5). The radius of the circle is blank units. The point (-7, blank) lies on this circle

Answers

It's important that you share the complete question. What is your goal here? Double check to ensure that you have copied the entire problem correctly.

The general equation of a circle is x^2 + y^2 = r^2. Here we know that the circle passes thru two points: (-3,2) and (1,5). Given that a third point on the circle is (-7, ? ), find the y-coordinate of this third point.

Subst. the known values (of the first point) into this equation: (-3)^2 + (2)^2 = r^2. Then 9 + 4 = 13 = r^2.

Let's check this. Assuming that the equation of this specific circle is
x^2 + y^2 = r^2 = 13, the point (1,5) must satisfy it.

(1)^2 + (5)^2 = 13 is not true, unfortunately.

(1)^2 + (5)^2 = 1 + 25 = 26 (very different from 13).

Check the original problem. If it's different from that which you have shared, share the correct version and come back here for further help.

one slice of cheese pizza contains 310 calories.A medium-size orange has one-fifth that number of calories. How many calories are in a medium-size orange?

Answers

310 dividedby 5. You do the math

slice of pizza has 310 calories
The orange has one-fifth of the pizza
So calories in orange = 310 ÷ 5 = 62 calories.

Your answer is 62 calories.

Hope it helped you. Mark as best!

which is the value that will make -7x<102

Answers

-7x < 102

First step is to divide both sides by -7. Because we are dividing by a negative number, we have to flip the signs.

-7x < 102
x > -102/7

The only one of your answer choices that is greater than -102/7 is A. 20.

Hope this helped!

The correct answer us 20. Option A.

how many sets of 4 consecutive numbers are there such that the product of the numbers is less than 100000

Answers

The answer is 4x(12)<100000

Please show the steps in solving B=5/7(F-38) solve for F

Answers

here's the answer for your problem

In your own words, explain the place value relationship when the same two digits are next to each other in a multi digit number.

Answers

i would help if i was smart.

Prove by PMI that
3^n >= 1+2^n

Answers

Hello,

[tex]If\ n=1\ then\ 3^1 \geq 1+2^1\ since\ 3 \geq 3\\ \textrm{This proves the base case.}\\ \textrm{Now assume this holds for some n = k.}\\ \textrm{We need to show this holds for n = k +1}\\ 3^k \geq 1+2^k\ is\ true.\\ 3^{k+1}=3*3^k \geq 3*(1+2^k)\\ 3^{k+1}=3+(1+2)*2^k=3+2^k+2^{k+1} \geq 3+2^{k+1}\\ 3^{k+1} \geq 1+2^{k+1}\ is\ true. [/tex]

what is critique reasoning

Answers

Critique reasoning involves systematically evaluating arguments, identifying assumptions, assessing evidence, and providing reasoned judgments.

Critical reasoning involves analyzing arguments or claims in a systematic and logical manner to evaluate their validity, soundness, and coherence. It entails examining evidence, identifying assumptions, assessing logical consistency, and recognizing fallacies.

Critique reasoning goes beyond merely accepting or rejecting a statement; it involves providing reasoned and well-supported judgments or critiques based on evidence and logical analysis. It helps individuals develop a deeper understanding of complex issues, make informed decisions, and construct persuasive arguments.

Critique reasoning fosters intellectual independence and the ability to engage critically with diverse perspectives and ideas.

What is 0.0004694 in scientific notation

Answers

It is 4.694 times 10^-4

This would be 4.694 * 10-4

If an experiment consists of five outcomes with p(o1) = 0.10, p(o2) = 0.20, p(o3) = 0.30, p(o4) = 0.15, then p(o5) is

Answers

Given an experiment with 5 trials, the sum of probabilities is 1.

i.e.
p(o1) + p(o2) + p(o3) + p(o4) + p(o5) = 1

0.10 + 0.20 + 0.30 + 0.15 + p(o5) = 1

0.75 + p(o5) = 1

p(o5) = 1 - 0.75 = 0.25

p(o5) = 0.25

the shortest adult women is 24 inches tall. the tallest adult women is 92 inches tall. write and absolute value equation to represent the minimum and maximum heights

Answers

The general equation of an absolute value equation is: |x - μ|, where μ is the mean and x is a single data point. The data points given are 24 and 92.

μ = (24 + 92)/2 = 58

Let's solve for |x - μ|:
|24 - 58| = 34
|92 - 58| = 34

Therefore, the absolute value equation is:
|x - 58| = 34

Find all real solutions
2x² + 4x + 1 = 0

Answers

This quadratic polynomial is unable to be factored, so we'll need to use the quadratic formula:
[tex]x=\frac{-b\pm \sqrt{(b^{2})-4ac}}{2a}[/tex]

Here a=2, b=4, c=1 so:
[tex]x=\frac{-4\pm \sqrt{(4^{2})-4*2*1}}{2*2}[/tex]

If you need help from there, let me know.

Which of the following is a factor of x^3-4x^2-18x+9

Answers

(x-2)(x^2-7x+3) most likely

Hello,

[tex]x^3-4x^2-18x+9\\ =x^3+3x^2-7x^2-21x+3x+9\\ =x^2(x+3)-7x(x+3)+3(x+3)\\ =(x+3)(x^2-7x+3)\\ =(x+3)(x- \frac{7- \sqrt{37}}{2} )(x- \frac{7+ \sqrt{37}}{2} )[/tex]

Select all that apply. (xyz)2 = _____ The expression without exponents is?

Answers

(xyz)² = x.x.y.y.z.z. This is this expression without exponents

Suppose that coin 1 has probability 0.7 of coming up heads, and coin 2 has probability 0.6 of coming up heads. if the coin flipped today comes up heads, then we select coin 1 to flip tomorrow, and it if comes up tails, then we select coin 2 to flip tomorrow. if the coin initially flipped is equally likely to be coin 1 or coin 2. what is the probability that the coin flipped after four transitions is coin

Answers

Answer:

C. 3/8

Step-by-step explanation:

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