Cole uses 2 1/4 cans of paint to paint 3/7 of his room. How many cans of paint will he use to paint the whole room? Emily rode the roller coaster at the amusement park and screamed... Cole uses 2 1/4 cans of paint to paint 3/7 of his room. How many cans of paint will he use to paint the whole room? Emily rode the roller coaster at the amusement park and screamed the entire time. After 3 1/3 minutes the ride was 7/9 complete. How long did the entire ride take, and how long did everyone have to suffer? Jake was downloading dance moves from fortnite to prepare for Friday Night. After 14 minutes the dance move was 3/11 complete. How long did Jake have to wait for his killed dance move? Read more

Steps to Solve

1. Determine total paint needed for the room

To find the total cans of paint for the entire room, set up a proportion using the information provided:

$$ \frac{2 \frac{1}{4}}{\frac{3}{7}} = \frac{x}{1} $$

Where $x$ is the total cans of paint needed for the entire room.

2. Convert mixed numbers to improper fractions

Convert (2 \frac{1}{4}) to an improper fraction:

$$ 2 \frac{1}{4} = \frac{9}{4} $$

Now the equation becomes:

$$ \frac{\frac{9}{4}}{\frac{3}{7}} = x $$

3. Cross-multiply to solve for x

Cross-multiplying gives:

$$ 9 \cdot 7 = 3 \cdot 4x $$

This simplifies to:

$$ 63 = 12x $$

4. Solve for x

Divide both sides by 12:

$$ x = \frac{63}{12} $$

5. Simplify the fraction

Simplify ( \frac{63}{12} ) to its simplest form:

$$ x = \frac{21}{4} = 5 \frac{1}{4} $$

So, Cole will use (5 \frac{1}{4}) cans of paint to paint the whole room.

6. Determine total time for the ride

Next, use the information given about the roller coaster ride. If (3 \frac{1}{3}) minutes is ( \frac{7}{9} ) of the ride, set up a proportion:

$$ \frac{3 \frac{1}{3}}{\frac{7}{9}} = \frac{t}{1} $$

Where (t) is the total time of the ride.

7. Convert mixed number to improper fraction

Convert (3 \frac{1}{3}) to an improper fraction:

$$ 3 \frac{1}{3} = \frac{10}{3} $$

So, the equation is:

$$ \frac{\frac{10}{3}}{\frac{7}{9}} = t $$

8. Cross-multiply to solve for t

Cross-multiplying gives:

$$ 10 \cdot 9 = 7 \cdot 3t $$

This simplifies to:

$$ 90 = 21t $$

9. Solve for t

Divide both sides by 21:

$$ t = \frac{90}{21} $$

10. Simplify the fraction

Simplify ( \frac{90}{21} ):

$$ t = \frac{30}{7} \approx 4 \frac{2}{7} \text{ minutes} $$

So, the entire ride took (4 \frac{2}{7}) minutes.

11. Determine wait time for the dance move

Lastly, for the dance move, given (14) minutes with ( \frac{3}{11} ) complete, set up:

$$ \frac{14}{\frac{3}{11}} = w $$

Where (w) is the total wait time for his fully downloaded dance move.

12. Cross-multiply to solve for w

Cross-multiply to solve for (w):

$$ 14 \cdot 11 = 3w $$

This simplifies to:

$$ 154 = 3w $$

13. Solve for w

Divide both sides by 3:

$$ w = \frac{154}{3} \approx 51 \frac{1}{3} \text{ minutes} $$

The wait time for his killed dance move was (51 \frac{1}{3}) minutes.