Rates & Ratios — Quiz 3

Questions in this quiz (9)

1. If $$(6\sqrt{2})^a=256^b$$ and $$a\neq0$$, $$b\neq0$$, what is the ratio $$\frac{a}{b}$$?

   • $$\frac{12}{5}$$
   • $$\frac{7}{5}$$
   • $$\frac{16}{3}$$
   • $$\frac{14}{5}$$

2. Two towns, Town X and Town Y, are located 15 miles apart in a straight line. A cyclist starts from Town X and travels toward Town Y at a constant speed of 5 miles per hour. How long will it take the cyclist to reach Town Y?

   • 1 hour
   • 2 hours
   • 3 hours
   • 4 hours

3. Two cars, driven by Alex and Mia, start 50 miles apart and drive toward each other on a straight road. Alex drives at a speed of 40 miles per hour, and Mia drives at a speed of 30 miles per hour. After how many minutes will Alex and Mia pass each other?

   • $$40$$
   • $$\frac{5}{7}$$
   • $$\frac{300}{7}$$
   • $$43.86$$

4. A storage tank can hold $$24000$$ liters of water when full. It will be filled by $$4$$ hoses, each of which pumps $$5$$ liters of water per minute. How many hours will it take to fill the tank?

   • $$15$$
   • $$30$$
   • $$20$$
   • $$25$$

5. A housing complex has only small and large houses. Renovation costs are $$5000$$ dollars for each small house and $$7500$$ dollars for each large house. If the ratio of small houses to large houses is $$4:1$$, renovation costs averaged how many dollars per house?

   • $$5800$$
   • $$6000$$
   • $$5500$$
   • $$6300$$

6. The ratio of the number of cubic units in the volume of a cube to the number of square units in the total surface area of the cube is 4:5. What is the total surface area of the cube?

   • $$138.24$$
   • $$208.45$$
   • $$158.44$$
   • $$119.64$$

7. The ratio of the number of linear units in the perimeter of a square to the number of square units in the area of that square is $$1:4$$. What is the length of a side of the square?

   • $$40$$
   • $$60$$
   • $$6$$
   • $$16$$

8. Suppose the intensity of light is inversely proportional to the square of the distance from the source. If the intensity is 80 units at 5 meters away, what is the intensity at 20 meters away?

   • 4
   • 5
   • 6
   • 7

9. Leo jogged a total of $$90$$ miles on a trail. $$\frac{1}{4}$$ of the distance was uphill, and $$\frac{3}{4}$$ of the distance was downhill. His average speed downhill was $$12$$ miles per hour, and the total time he spent jogging was $$9$$ hours. What was his average uphill speed?

   • 11.5
   • 6.67
   • 8.75
   • 9.13