Rates & Ratios — Quiz 4

Questions in this quiz (10)

1. 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?

   • 30
   • 0.99
   • 0.624
   • 1.20

2. 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?

   • 6:00 PM
   • 5:56 PM
   • 3:55 PM
   • 2:00 PM

3. 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?

   • 120
   • 314
   • 50
   • 360

4. 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?

   • $$\frac{49}{10}$$
   • $$\frac{49}{360}$$
   • $$\frac{49}{12}$$
   • $$\frac{49}{3}$$

5. 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?

   • 1:2
   • 1:4
   • 1:1
   • 1:8

6. 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?

   • $$40$$
   • $$25$$
   • $$30$$
   • $$39$$

7. 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?

   • $$\frac{3}{5}$$
   • $$\frac{2}{5}$$
   • $$\frac{80}{255}$$
   • $$\frac{51}{100}$$

8. 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?

   • $$34$$
   • $$67$$
   • $$33$$
   • $$60$$

9. 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?

   • $$10.2$$
   • $$30$$
   • $$40.2$$
   • $$50.8$$

10. 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 $$b$$?

    • $$6:1$$
    • $$4:3$$
    • $$3:2$$
    • $$3:4$$