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Rates, SM-Bank 098

The distance-time graph below shows Betty's train trip to her Grandmother's house in the Blue Mountains and the return journey in her Grandmother's car.

  1. Which section of the the graph shows where Betty had to change trains and wait to catch the next train?  (1 mark)

  2. How long did Betty take to complete section C?  (1 mark)

  3. After how many hours did Betty reach her Grandmother's house?  (1 mark)

  4. What was Betty's average speed for section D?  (2 marks)

  5. How many kilometres did Betty travel in total?  ( 2 marks)

  6. What was Betty's average speed for the entire trip?  (2 marks)

  7. Which section of the graph is the steepest? What can you say about Betty's speed in this section? (2 marks)

Show Answers Only

a.    \(\textit{B}\)

b.    \(1 \text{ hour}\)

c.    \(2.5 \text{ hours}\)

d.    \(80\ \text{km/h}\)

e.    \(240\ \text{km}\)

f.     \(60\ \text{km/h}\)

g.    \(\text{The graph was steepest in Section }\textit{A}.\)

\(\text{This is where Betty was travelling the fastest.}\)

Show Worked Solution

a.    \(\text{Horizontal sections of the graph indicate the person}\)

\(\text{is not moving.}\)

\(\therefore\ \text{Betty waited for the next train in section}\ \textit{B}.\)

b.    \(1 \text{ hour}\)

c.    \(2.5 \text{ hours}\)

d.    
\(\text{Speed}\) \(=\dfrac{\text{Distance}}{\text{Time}}\)
    \(=\dfrac{120}{1.5}\)
    \(=80\ \text{km/h}\)

 
e.    \(\text{Total distance}=2\times 120=240\ \text{km}\)

f.    
\(\text{Speed}\) \(=\dfrac{\text{Distance}}{\text{Time}}\)
    \(=\dfrac{240}{4}\)
    \(=60\ \text{km/h}\)

 
g.    \(\text{The graph was steepest in Section }\textit{A}.\)

\(\text{This is where Betty was travelling the fastest.}\)