Choose an appropriate metric unit for the mass of bowling ball

Ben, Tim, and Sam have to do a certain job. Ben can finish the job in 5 hours. Tim can finish the job in 6 hours. Sam can finish

Brut [27]

x is 7.5 hours

Step-by-step explanation:

Ben, Tim, and Sam have to do a certain job

Ben can finish the job in 5 hours
Tim can finish the job in 6 hours
Sam can finish the job in x hours
The three of them can finish the job in 2 hours if they work together

We need to find x

∵ Ben can finish the job in 5 hours

∴ The rate of Ben = $\frac{1}{5}$

∵ Tim can finish the job in 6 hours

∴ The rate of Tim = $\frac{1}{6}$

∵ Sam can finish the job in x hours

∴ The rate of Sam = $\frac{1}{x}$

They will working together to finish the job in two hours, that means the sum of their rate is equal to 1/2

∵ They can finish the job in 2 hours if they work together

∴ $\frac{1}{5}+\frac{1}{6}+\frac{1}{x}=\frac{1}{2}$

To add the fractions find the LCM for all denominators to make all fractions with same denominators

∵ The LCM of 5, 6 ans x is (5 × 6 × x) = 30 x,

- Divide it by each denominator to find the new numerators

∵ 30 x ÷ 5 = 6 x , 30 x ÷ 6 = 5 x , 30 x ÷ x = 30

- Change all the denominators to 30 x and then write the new

numerators of each fraction

∴ $\frac{6x}{30x}+\frac{5x}{30x}+\frac{30}{30x}=\frac{1}{2}$

Add the numerators and put the sum over 30 x

∵ $\frac{11x+30}{30x}=\frac{1}{2}$

- By using cross multiplication

∴ 2(11 x + 30) = 1(30 x)

- Simplify the both sides

∴ 22 x + 60 = 30 x

- Subtract 22 x from both sides

∴ 60 = 8 x

- Divide both sides by 8

∴ 7.5 = x

∴ The value of x is 7.5 hours

x is 7.5 hours

Learn more:

You can learn more about the word problems in brainly.com/question/10712420

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5 0

3 years ago

Write an equation of the line, in slope intercept form.

DedPeter [7]

Answer:

y = -3x + 6

Step-by-step explanation:

Slope-intercept form:

y = mx + b

m (slope) = $\frac{-6}{2}$ or -3

b (y-intercept, or where the line crosses the y-axis) = 6

y = -3x + 6

4 0

3 years ago

Read 2 more answers

500=100(x-1) Someone tell me step by step

Andre45 [30]

First, distribute the 100 to the (x-1) portion:
500 = 100x - 100

then, add 100 to both sides of your equation to get “x” alone on the right side:
500 + 100 = 100x - 100 + 100
600 = 100x

next, divide 100x by 100 and 600 by 100 to isolate a singular “x”:
600/100 = 100x/100
6 = x

therefore, x=6 is your solution

5 0

2 years ago

estamos construyendo una carretera que enlace los puntos a = 12 ,21 y b =(17,23) otro punto se encuentra en c =(3,9) es posible

Nadusha1986 [10]

Answer:

is not possible

Step-by-step explanation:

The question in English is

we are building a road that links the points a = (12 ,21) and b =(17,23) another point is in c =(3,9) it is possible that a single road allows to join these three points?

we know that

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

step 1

Find the slope ab

we have

a = (12 ,21) and b =(17,23)

substitute

$m=\frac{23-21}{17-12}$

$m=\frac{2}{5}$

step 2

Find the slope ac

we have

a = (12 ,21) and c =(3,9)

substitute

$m=\frac{9-21}{3-12}$

$m=\frac{-12}{-9}$

simplify

$m=\frac{4}{3}$

step 3

Compare slopes ab and ac

The slopes are different

That means ----> is not possible that a single road allows to join these three points

7 0

3 years ago

Carson needs 3 quarts of water to make fruit punch, but has only a l-cup measuring cup.

olga_2 [115]

Answer:

Cups of water she needs to make the punch is 12.

Step-by-step explanation:

Amount of water Carson need to make fruit punch = 3 quarts

2 cups is 1 pint

2 pints is 1 quart

1 pint = 1/2 quarts

2 cups is 1 pint which is 1/2 quarts

So, 1 cup:

1 cup is 1/2 times 2 quarts

1 quart is 1 times 2 times 2 cups equals 4 cups

So, 3 quarts equals 3 times 4 cups which equals 12 cups.

So it is 12 cups.

7 0

4 years ago