2. Ratios, Rates, and Proportions (N)
  3. Lesson 11: Rates and Proportional Relationships

Exercises


  1. Arlie describes an after-hours cleaning service using the equation\[C = 24 n\] where \(n\) is the number of offices in the building and \(C\) is the cost for cleaning, in dollars. Yannic has a similar cleaning service that advertises a fee of \($ 280\) for \(10\) offices. Which cleaning service offers the best deal?
  2. Which of the following represents the greatest speed? 
    1. \(25\) km/h
    2. A graph with Time in hours along the horizontal axis and Distance in kilometres along the vertical axis. Four points are plotted at (5,150), (10,300), (15,450), and (20,600).
    3. Time (h) Distance (km)
      \(2\) \(40\)
      \(4\) \(80\)
      \(6\) \(120\)
  3. Which of the following represents the most efficient auto repair shop?
    1. \(115\) cars per week while working \(7\) days in a week.
    2. A graph with Time in days along the horizontal axis and Number of Cars along the vertical axis. Five points are plotted at (1,16), (2,32), (3,48), (4,64), and (5,80).
    3. Number of Cars Time
      \(30\) \(2\) days
      \(60\) \(4\) days
      \(90\) \(6\) days
  4. Which of the following animals is the slowest?
    1. At top speed, a garden snail can travel \(1\) km in \(10\) hours.
    2. The following graph shows a tortoise moving at its top speed.
      A graph with Time in minutes along the horizontal axis and Distance in metres along the vertical axis. Five points are plotted at (1,5), (2,10), (3,15), (4,20), and (5,25).
    3. The following table tracks a sloth moving at its top speed.
      Distance (cm) Time (s)
       \(0\) \(0\)
      \(16.5\) \(5\)
      \(33\) \(10\)
  5. Three different relationships between proportional quantities \(x\) and \(y\) are being described in the parts below.
    1. \(y = 1.6x\)
    2. An increase of \(4\) in the value of \(x\) always results in an increase of \(7\) in the value of \(y\).
    3. \(x\) \(y\)
      \(1.5\) \(2.55\)
      \(3\) \(5.1\)
      \(4.5\) \(7.65\)
    If each relationship is graphed with the same scale, then which graph will be the steepest? Which graph will be the least steep?
  6. The flow rates for three different hoses are being compared below. Approximately how many hours will it take the fastest hose to fill a \(40~000\) L pool? How about the slowest hose?
    1. \(22.7\) L/min
    2. \(V =1580 t\) where \(V\) is the volume of water in litres, and \(t\) is the time in hours.
    3. A graph with Time in minutes along the horizontal axis and Volume in millilitres along the vertical axis. Four points are plotted at (1,25000), (2,50000), (3,75000), and (4,100000).
  7. At one store, square tiles measuring \(10\) cm by \(10\) cm are sold at a rate of \($2.80\) for \(8\) tiles. At another store, square tiles are sold at \($40.00\) per square metre. What is the cheapest possible price to tile a \(25\) square metre floor?
  8. Tickets for the local symphony have an average price of \($45\) per ticket, and tickets to see the local baseball team have an average price of \($22\) per ticket. To increase the number of attendees at the symphony, a promotion has been planned where the average price of symphony tickets will decrease by \(x \%\) . At the same time, the price for the baseball tickets will be increased by \(x \%\) for the same \(x\). Is there a value of \(x\) for which the two updated average ticket prices will be equal?