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4"},"content":{"rendered":""},"excerpt":{"rendered":""},"featured_media":0,"featured_media_url":"$undefined","acf":{"duree_estimee":10,"niveau_difficulte":"Advanced","categorie":"Rates & Ratios","nombre_questions":10,"score_minimum":78,"ordre_questions":"Fixe","questions":[{"id":"cmmek27790055k004ujybcfrd","texte_question":"

A point on the rim of a wheel with a radius of 80 meters travels 50 meters in 30 seconds. How many degrees per second does the wheel rotate?

","type_question":"QCM","explication":"$17","points":1,"temps_limite":"$undefined","reponses":[{"texte":"30","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

0.99

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

0.624

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

1.20

","correcte":true,"explication":"","imageUrl":"$undefined"}]},{"id":"cmmek2779005ak004692xn3oc","texte_question":"

A pool is enclosed between two concentric circles with radii of 10 and 15 meters and has a depth of 3 meters. If the pool is empty at 2:00 PM and is filled at a rate of 5 cubic meters per minute, at what time, to the nearest minute, will the pool first be full?

","type_question":"QCM","explication":"","points":1,"temps_limite":"$undefined","reponses":[{"texte":"6:00 PM","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"5:56 PM","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

3:55 PM

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

2:00 PM

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmmek2779005fk0041j67s1ls","texte_question":"

A merry-go-round with a radius of 50 feet rotates at a speed of 3 degrees per second. How many feet does a point on the edge of the merry-go-round, farthest from the center, travel in 2 minutes?

","type_question":"QCM","explication":"$18","points":1,"temps_limite":"$undefined","reponses":[{"texte":"120","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

314

","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

360

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmmek2779005kk004avawneut","texte_question":"

What fraction of a 12-inch pie contains the same amount of filling as a slice of a 14-inch pie cut into 10 equal slices, assuming both pies have the same thickness?

","type_question":"QCM","explication":"

Let the radius of the 12-inch pie be:

$$r_1 = \\frac{12}{2} = 6$$

Let the radius of the 14-inch pie be:

$$r_2 = \\frac{14}{2} = 7$$

Step 1: Find the area of one slice of the 14-inch pie

Each slice is one-tenth of the whole:

$$\\text{Area}_{\\text{slice}} = \\frac{\\pi r_2^2}{10} = \\frac{\\pi (7)^2}{10} = \\frac{49\\pi}{10}$$

Step 2: Let the fraction of the 12-inch pie be $$x$$.

The area of this fraction is:

$$\\text{Area}_{\\text{fraction}} = x \\cdot \\pi r_1^2 = x \\cdot \\pi (6)^2 = 36x\\pi$$

Step 3: Set the two areas equal:

$$36x\\pi = \\frac{49\\pi}{10}$$

Divide both sides by $$\\pi$$:

$$36x = \\frac{49}{10}$$

Solve for $$x$$:

$$x = \\frac{49}{360}$$

Final Answer: $$\\frac{49}{360}$$

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"

$$\\frac{49}{10}$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$\\frac{49}{360}$$

","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$\\frac{49}{12}$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$\\frac{49}{3}$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmmek2779005pk004njaj5q3r","texte_question":"

In the following figure, each circle is tangent to the other two circles, and the two shaded circles are identical to each other. What is the ratio of the shaded region to the nonshaded region?

","type_question":"QCM","explication":"$19","points":1,"temps_limite":"$undefined","reponses":[{"texte":"1:2","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"1:4","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

1:1

","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

1:8

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmmek277a005uk004wd6stbs0","texte_question":"

Liam and his friend Noah were racing on a 400-meter track. Noah started running first, and Liam didn’t start until Noah had completed half a lap. Liam passed Noah at the exact moment they both finished their seventh lap. If both ran at constant speeds, with Liam running 3 meters per second faster than Noah, what was Noah's speed in meters per second?

","type_question":"QCM","explication":"$1a","points":1,"temps_limite":"$undefined","reponses":[{"texte":"

$$40$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$25$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$30$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$39$$

","correcte":true,"explication":"","imageUrl":"$undefined"}]},{"id":"cmmek277a005zk0044biino05","texte_question":"

There are $$300$$ students at Greenwood High, where the ratio of sophomores to seniors is $$5:7$$. There are $$200$$ students at Lincoln High, where the ratio of sophomores to seniors is $$3:2$$. The two schools hold a combined event, and all the sophomores and seniors from both schools attend. What fraction of the students at the event are seniors?

","type_question":"QCM","explication":"$1b","points":1,"temps_limite":"$undefined","reponses":[{"texte":"

$$\\frac{3}{5}$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$\\frac{2}{5}$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$\\frac{80}{255}$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$\\frac{51}{100}$$

","correcte":true,"explication":"","imageUrl":"$undefined"}]},{"id":"cmmek277a0064k0043xzazfen","texte_question":"

Lisa and John are working together to review $$72$$ reports. Lisa can review $$4$$ reports per hour, and John can review $$5$$ reports per hour. If Lisa starts reviewing first and John joins her three hours later, how many reports will John have reviewed by the time they finish?

","type_question":"QCM","explication":"

Step 1: Determine how many reports Lisa reviews before John starts

Lisa works alone for $$3$$ hours and reviews:

$$3 \\cdot 4 = 12$$ reports

Step 2: Determine the remaining reports

Total reports: $$72$$

Reports already reviewed: $$12$$

Remaining:

$$72 - 12 = 60$$ reports

Step 3: Determine their combined work rate

Lisa and John together review:

$$4 + 5 = 9$$ reports per hour

Step 4: Time to finish remaining reports

Time to review $$60$$ reports at $$9$$ reports per hour:

$$\\frac{60}{9} = \\frac{20}{3}$$ hours

Step 5: Reports John reviews during that time

John works $$\\frac{20}{3}$$ hours at $$5$$ reports per hour:

$$5 \\cdot \\frac{20}{3} = \\frac{100}{3}$$ reports

Final Answer: 33 reports

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"$$$34$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$67$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$33$$

","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$60$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmmek277a0069k004g0iulsb6","texte_question":"

The ratio of the side lengths of a triangle is exactly $$5:8:10$$. In a second triangle similar to the first, the shortest side is $$15$$ inches long. To the nearest tenth of an inch, what is the length of the longest side of the second triangle?

","type_question":"QCM","explication":"

Let the scale factor between the two triangles be $$k$$.

The shortest side in the first triangle is $$5$$, and the shortest side in the second triangle is $$15$$. So:

$$k = \\frac{15}{5} = 3$$

Since the triangles are similar, all sides are scaled by the same factor. The longest side in the first triangle is $$10$$, so the corresponding side in the second triangle is:

$$10 \\cdot 3 = 30$$

Final Answer: $$30$$

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"

$$10.2$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$30$$

","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$40.2$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$50.8$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmmek277a006ek004uqseb204","texte_question":"

Let $$a$$ and $$b$$ be numbers such that $$a$$ and $$b$$ are both nonzero and $$a$$ > $$b$$. If one-third of $$a$$ is equal to forty percent of the positive difference between $$a$$ and $$b$$, then what is the ratio of $$a$$ to $$b$$?

","type_question":"QCM","explication":"

Step 1: Set Up the Equation

We are given that:

$$\\frac{1}{3}a = 0.4(a-b)$$

Step 2: Solve for $$a/b$$

Multiply both sides by 3 to eliminate the fraction:

$$a = 1.2(a-b)$$

Expanding the right-hand side:

$$a = 1.2a - 1.2b$$

Rearrange to isolate $$b$$:

$$a - 1.2a = -1.2b$$

$$-0.2a = -1.2b$$

Divide by $$-0.2$$:

$$a = 6b$$

Thus, the ratio of $$a$$ to $$b$$ is:

$$\\frac{a}{b} = 6$$

So, the ratio of $$a$$ to $$b$$ is 6:1.

Final Answer: 6:1

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"

$$6:1$$

","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"$$$4:3$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$3:2$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$3:4$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]}]},"categories":["rates-ratios"],"date":"2026-02-17T02:29:44.013Z","modified":"2026-03-06T07:10:42.933Z"}}]]}]}]]