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Alexeev081 [22]

3 years ago

5

Xanthia can read 100 pages per hour and Molly can read 50 pages per hour. If they each read the same book, and the book has 225

pages, how many more minutes than Xanthia would it take for Molly to finish reading the book?

2 answers:

Alexus [3.1K]3 years ago

6 0

Answer:

135 mins

Step-by-step explanation:

Reading the book takes Xanthia

$\frac{225}{100}=2.25$ hours.

It takes Molly

$\frac{225}{50}=4.5$ hours.

The difference is $2.25$ hours, or $2.25(60)=\boxed{135}$ minutes.

Talja [164]3 years ago

4 0

Answer:

135 minutes

Step-by-step explanation:

Let

y -----> the number of pages to finish reading the book

x ----> the number of hours

we know that

The linear equation in slope intercept form is equal to

$y=mx+b$

where

m is the unit rate or slope of the linear equation

b is the y-intercept or initial value

In this problem we have

<em>Xanthia</em>

$m=100\ pages/hour$

$b=225\ pages$

$y=-100x+225$ ----> the slope is negative because is a decreasing function

For y=0

substitute and solve for x

$0=-100x+225$

$100x=225$

$x=2.25\ hours$ ---> Xanthia's time to finish reading the book

<em>Molly</em>

$m=50\ pages/hour$

$b=225\ pages$

$y=-50x+225$ ----> the slope is negative because is a decreasing function

For y=0

$0=-50x+225$

$50x=225$

$x=4.5\ hours$ --- Molly's time to finish reading the book

To find out how many more minutes than Xanthia would it take for Molly to finish reading the book, subtract Xanthia's time from Molly's time

$4.5\ h-2.25\ h=2.25\ h$

Convert to minutes

Multiply by 60

$2.25\ h=2.25(60)=135\ minutes$

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$\implies r(r-1)x^r+6rx^r+4x^r=0$
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so the characteristic solution is

$y_c=\dfrac{C_1}x+\dfrac{C_2}{x^4}$

As a guess for the particular solution, let's back up a bit. The reason the choice of $y=x^r$ works for the characteristic solution is that, in the background, we're employing the substitution $t=\ln x$ , so that $y(x)$ is getting replaced with a new function $z(t)$ . Differentiating yields

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac1x\dfrac{\mathrm dz}{\mathrm dt}$
$\dfrac{\mathrm d^2y}{\mathrm dx^2}=\dfrac1{x^2}\left(\dfrac{\mathrm d^2z}{\mathrm dt^2}-\dfrac{\mathrm dz}{\mathrm dt}\right)$

Now the ODE in terms of $t$ is linear with constant coefficients, since the coefficients $x^2$ and $x$ will cancel, resulting in the ODE

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$u_1=-\displaystyle\int\frac{z_2e^{2t}\sin e^t}{W(z_1,z_2)}\,\mathrm dt$
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