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3 years ago

15

Caroline and Chase are working on math homework. They decide to race to see who can finish first. Caroline is on number 12 and c

an solve 1 math problem in 1.5 minutes. Chase is on number 16 and can solve 1 math problem in 2 minutes. How many minutes will it take before they are on the same problem?

1 answer:

tiny-mole [99]3 years ago

6 0

Answer:

It will take 24 minutes before they are on the same problem.

Step-by-step explanation:

Caroline is on number 12 and can solve 1 math problem in 1.5 minutes.

Per minute, she solved $\frac{1}{1.5} = \frac{2}{3}$ of a problem. So, after t minutes, she will be on the problem:

$Ca(t) = 12 + \frac{2t}{3}$

Chase is on number 16 and can solve 1 math problem in 2 minutes.

Per minute, he solved $\frac{1}{2}$ of a problem. So, after t minutes, he will be on the problem:

$Ch(t) = 16 + \frac{t}{2}$

How many minutes will it take before they are on the same problem?

This is t for which:

$Ca(t) = Ch(t)$

So

$12 + \frac{2t}{3} = 16 + \frac{t}{2}$

$\frac{2t}{3} - \frac{t}{2} = 4$

$\frac{4t-3t}{6} = 4$

$\frac{t}{6} = 4$

$t = 24$

It will take 24 minutes before they are on the same problem.

You might be interested in

6-4x=6x-8x+8<br><br> find the value of x

ad-work [718]

Answer:

x = -1

Step-by-step explanation:

6 − 4x = 6x − 8x + 8

Combine 6x and −8x to get −2x.

6 − 4x = −2x + 8

Add 2x to both sides.

6 − 4x + 2x = 8

Combine −4x and 2x to get −2x.

6 − 2x = 8

Subtract 6 from both sides.

−2x = 8 − 6

Subtract 6 from 8 to get 2.

−2x = 2

Divide both sides by −2.

$x = \frac{2}{-2}$

Divide 2 by −2 to get −1.

$x = 1$

Hope this helps and have a great day! =D

7 0

2 years ago

Read 2 more answers

It takes 4 hours to go fly to Atlanta, a city that is about 200 miles. How many miles have I flown in in 2.5 miles

Irina-Kira [14]

Answer:

x = 125

Step-by-step explanation:

4 hrs : 200 mi

2.5 hrs : x mi

4/2.5 = 1.6 hrs

200/1.6 = 125 mi

x = 125 mi

5 0

3 years ago

Find the surface area of the solid. Round to two decimal places

Ne4ueva [31]

Check the picture below.

so, to get the area of the triangles, we can simply run a perpendicular line from the top to the base, and end up with a right-triangle with a base of 22 and a hypotenuse of 34, let's find the altitude.

$\bf \textit{using the pythagorean theorem}
\\\\
c^2=a^2+b^2\implies \sqrt{c^2-a^2}=b
\qquad 
\begin{cases}
c=hypotenuse\\
a=adjacent\\
b=opposite\\
\end{cases}
\\\\\\
\sqrt{34^2-22^2}=b\implies \sqrt{672}=b$

so then the surface area of the triangular prism is,

$\bf \stackrel{\textit{left and right}}{2(34\cdot 76)}~~+~~\stackrel{\textit{bottom}}{(44\cdot 76)}~~+~~\stackrel{\textit{front and back}}{2\left[\cfrac{1}{2}(44)(\sqrt{672}) \right]}
\\\\\\
8512~~+~~(44)(\sqrt{672})\qquad \approx\qquad 9652.61036291978$

5 0

3 years ago

Amelia, Luis, Shauna, and Clarence used different approaches to solve the inequality

Mama L [17]

Answer:

Luis’s, because he flipped the inequality sign when he subtracted

Step-by-step explanation:

Given:

7.2b + 6.5 > 4.8b – 8.1.

Amelia started by subtracting 7.2b from both sides to get 6.5 > –2.4b – 8.1.

Amelia:

7.2b + 6.5 - 7.2b > 4.8b – 8.1 - 7.2b

6.5 > -2.4b - 8.1

Correct

Luis started by subtracting 4.8b from both sides to get 2.4b + 6.5 < – 8.1.

7.2b + 6.5 - 4.8b > 4.8b – 8.1 - 4.8b

2.4b + 6.5 > -8.1

Incorrect

Shauna started by subtracting 6.5 from both sides to get 7.2b > 4.8b – 14.6

7.2b + 6.5 - 6.5 > 4.8b – 8.1 - 6.5

7.2b > 4.8b - 14.6

Correct

Clarence started by adding 8.1 to both sides to get 7.2b + 14.6 > 4.8b.

7.2b + 6.5 + 8.1 > 4.8b – 8.1 + 8.1

7.2b + 14.6 > 4.8b

Correct

5 0

2 years ago

What is the interest rate of each investment if The annual interest on a $17,000 investment exceeds the interest earned on an $8

Butoxors [25]

<u>Solution-</u>

Let's assume, the rate of interest of $8000 is x%,

then the rate of interest of $17000 is (x+0.3x) =1.3x%

Interest earned by $8000,

$i_1=\frac{8000\times x\times 1}{100} =80x$

Interest earned by $17,000,

$i_2=\frac{17000\times 1.3x\times 1}{100} =221x$

According to the question,

$\Rightarrow i_1=i_2+276$

$\Rightarrow 221x=80x+276$

$\Rightarrow 221x-80x=276$

$\Rightarrow 141x=276$

$\Rightarrow x=1.96$

∴ Rate of interest of $8000 is 1.96% and rate of interest of $17000 is (1.3×1.96) =2.55%

3 0

3 years ago