Ask question

Ask question

All categories

2 years ago

13

A boat moves at a rate of 11 mph in still water. If the river's current flows at a rate of 3 mph, how long does it take the boat

to travel 27 miles upstream?
It takes hours.
(Round to the nearest tenth.)

2 answers:

Sergio [31]2 years ago

8 0

Answer:

2 hrs

Step-by-step explanation:

Boat moving rate= 11 mph

river's current flow rate= 3 mph

By adding both of them, we get

11 + 3 mph=14 mph

Now,

Time taken= distance travelled/ velocity

= 27/14

= 2 hrs

aev [14]2 years ago

8 0

Answer:

<u>It will take 3 hours 24 minutes or 3.4 hours (rounding to the nearest tenth) the boat to travel 27 miles upstream</u>

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Speed of the boat in still water = 11 mph

Speed of the river's current = 3 mph

Distance of the travel = 27 miles upstream

2. How long does it take the boat to travel?

x = Time it takes the boat to travel 27 miles upstream

Let's recall that Speed = Distance/Time, therefore,

Time = Distance/Speed

Now, let's solve for x in the following equation:

x = Distance of the travel/(Speed of the boat in still water - Speed of the river's current)

Explanation: We subtract the speed of the river's current because the boat is traveling upstream or against the current

Replacing with the values we know, we have:

x = 27/11 - 3

x = 27/8

x = 3.375 or 3 hours 22 minutes and 30 seconds (0.375 of an hour = 0.375 * 60 = 22.5)

<u>It will take 3 hours 24 minutes or 3.4 hours (rounding to the nearest tenth) the boat to travel 27 miles upstream</u>

You might be interested in

Find the absolute maximum and absolute minimum of the function f(x,y)=2x3+y4f(x,y)=2x3+y4 on the region {(x,y)|x2+y2≤64}{(x,y)|x

ddd [48]

Check where the first-order partial derivatives vanish to find any critical points within the given region:

$f(x,y)=2x^3+y^4\implies\begin{cases}f_x=6x^2=0\\f_y=4y^3=0\end{cases}\implies(x,y)=(0,0)$

The Hessian for this function is

$\mathbf H(x,y)=\begin{bmatrix}f_{xx}&f_{xy}\\f_{yx}&f_{yy}\end{bmatrix}=\begin{bmatrix}12x&0\\0&12y^2\end{bmatrix}$

with $\det\mathbf H(0,0)=0$ , so unfortunately the second partial derivative test fails. However, if we take $x=0$ we see that $f(x,y)>0$ for different values of $y$ ; if we take $y=0$ we see $f(x,y)$ takes on both positive and negative values. This indicates (0, 0) is neither the site of an extremum nor a saddle point.

Now check for points along the boundary. We can parameterize the boundary by

$(x,y)=(8\cos t,8\sin t)$

with $0\le t\le2\pi$ . This turns $f(x,y)$ into a univariate function $F(t)$ :

$F(t)=f(8\cos t,8\sin t)=2^{10}\cos^3t+2^{12}\sin^4t$

$\implies F'(t)=3\cdot2^{10}\cos^2t(-\sin t)+2^{14}\sin^3t\cos t=2^{10}\sin t\cos t(16\sin^2t-3\cos t)$

$F'(t)=0\implies\begin{matrix}\sin t=0\implies t=0,\,t=\pi\\\\\cos t=0\implies t=\dfrac\pi2,\,t=\dfrac{3\pi}2\\\\16\sin^2t-3\cos t=0\implies t=2\tan^{-1}\sqrt{\dfrac{\sqrt{1033}-32}3},\,t=2\pi-2\tan^{-1}\sqrt{\dfrac{\sqrt{1033}-32}3}\end{matrix}$

At these critical points, we get

$F(0)=1024$

$F\left(2\tan^{-1}\sqrt{\dfrac{\sqrt{1033}-32}3}\right)\approx893$

$F\left(\dfrac\pi2\right)=4096$

$F(\pi)=-1024$

$F\left(\dfrac{3\pi}2\right)=4096$

$F\left(2\pi-2\tan^{-1}\sqrt{\dfrac{\sqrt{1033}-32}3}\right)\approx893$

We only care about 3 of these results.

$t=\dfrac\pi2\implies(x,y)=(0,8)$

$t=\pi\implies(x,y)=(-8,0)$

$t=\dfrac{3\pi}2\implies(x,y)=(0,-8)$

So to recap, we found that $f(x,y)$ attains

a maximum value of 4096 at the points (0, 8) and (0, -8), and
a minimum value of -1024 at the point (-8, 0).

6 0

3 years ago

Study the following production possibility curve. The number of data points that illustrate the proper allocation of resources i

goldenfox [79]

The answer is three, I hope I helped :)

5 0

2 years ago

Read 2 more answers

James is setting up a fish tank. He is buying a breed of goldfish that typically grows to be 12 inches long . It's recommended t

ASHA 777 [7]

12:12 is the ratio because each fish can grow up to be 12 inches long so 12 gallons would be in the tank per fish.

4 0

3 years ago

Twenty-two less than three times a number is -70 translate into an equation.

adoni [48]

Answer:

987

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

What’s the answer to 14 and 18?

Shkiper50 [21]

14)

-√9/100 = -3/10

18)

-√2.25 = - 1.5

6 0

3 years ago

Read 2 more answers