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Rates, SM-Bank 079 MC

Sandra is counting the cars heading south on the highway through her town.

She observes that 1 car passes every 6 seconds.

If Sandra is counting for 2 hours at this rate, how many cars does she count?

  1. 600
  2. 720
  3. 1200
  4. 1440
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\(C\)

Show Worked Solution

\(1\text{ car/}6\ \text{seconds}=10\text{ cars/}\text{minute}\)

\(\therefore\ \text{Cars in 2 hours}\) \(=2\times 10\times 60\)
  \(=1200\)

\(\Rightarrow C\)

Rates, SM-Bank 078

The hardware store is having a sale on ladders.

They make $1800 from selling 3 ladders.

All ladders on sale cost the same.

How much will the hardware store make if they sell 8 ladders?  (2 marks)

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\($4800\)

Show Worked Solution
\(\text{Price per ladder}\) \(=\dfrac{1800}{3}\)
  \(=$600\)

 

\(\text{Price of 8 ladders}\) \(=8\times $600\)
  \(=$4800\)

Rates, SM-Bank 055

Jesse sells, an average of 150 roller-coaster tickets every 10 minutes.  How long will it take him sell 600 tickets?  (2 marks)

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\(40\ \text{minutes}\)

Show Worked Solution
\(10\ \text{minutes}/150\ \text{tickets}\) \(=\dfrac{10}{150}\ \text{minutes}/\dfrac{150}{150}\ \text{tickets}\)
  \(=\dfrac{1}{15}\ \text{minute}/1\ \text{ticket}\)
  \(=\bigg(\dfrac{1}{15}\times 600\bigg)\ \text{minutes}/600\ \text{tickets}\)
  \(=40\ \text{minutes}/600\ \text{tickets}\)

 
\(\therefore\ \text{It would take}\ 40\ \text{minutes to sell}\ 600\ \text{tickets.}\)

Rates, SM-Bank 048

Zach is saving money every year. The graph shows how much money is in his bank account at the end of each year.
 


 

What was Zach's average amount of money saved per year during the first 5 years?  (2 marks)

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\($120\text{/year}\)

Show Worked Solution
\(\text{Average saved per year}\) \(=\dfrac{\text{Money at Y5}}{\text{time}}\)
  \(= \dfrac{600}{5}\)
  \(= $120\text{/year}\)

Rates, SM-Bank 007

A young echidna weighed 1200 grams at the beginning of November just before leaving the burrow. 

At the end of March it weighed 1850 grams.

Calculate the average rate of growth of the echidna for the 5 month period.  (2 marks)

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\(130\ \text{g}/ \text{month}\)

Show Worked Solution
\(\text{Growth}\) \(=1200-1850\)
  \(=650\ \text{g}\)

 

\(\text{Rate of growth}/\text{month}\) \(=\dfrac{650}{5}\ \text{g}/\text{month}\)
  \(=130\ \text{g}/\text{month}\)

 

Rates, SM-Bank 005

A tree was 143 cm tall at the beginning of January.  At the end of May it measured 233 cm tall.

  1. Calculate the average rate of growth of the tree for the 5 month period.  (2 marks)

  2. If this rate of growth were to continue, how many more months would it take the tree to reach a height of 611 cm?  (2 marks)

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a.    \(18\ \text{cm}/ \text{month}\)

b.    \(21\ \text{months}\)

Show Worked Solution
a.    \(\text{Growth}\) \(=233-143\)
    \(=90\ \text{cm}\)

 

\(\text{Rate of growth}/\text{month}\) \(=\dfrac{90}{5}\ \text{cm}/\text{month}\)
  \(=18\ \text{cm}/\text{month}\)

 

b.    \(\text{Growth}\) \(=611-233\)
    \(=378\ \text{cm}\)
     
  \(\text{Months}\) \(=\dfrac{378}{18}\)
    \(=21\)

 
\(\therefore\ \text{It would take}\ 21\ \text{months for the tree to grow to a height of }\ 611\ \text{cm.}\)