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v1 Algebra, STD2 A1 2012 HSC 15 MC

A car takes 5 hours to complete a journey when travelling at 75 km/h.

How long would the same journey take if the car were travelling at 100 km/h?

  1. 37.5 minutes
  2. 1 hour and 20 minutes
  3. 3 hours and 45 minutes
  4. 4 hours and 15 minutes
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\(C\)

Show Worked Solution

\(T=\dfrac{D}{S}\)

\(\text{Since}\ \ \ T = 5\ \ \text{when}\ \ \ S = 75\)

\(5\) \(=\dfrac{D}{75}\)
\(D\) \(=5\times 75\)
  \(=375\ \text{km}\)

 

\(\text{Find}\ \ T\ \ \text{when}\ \ \ S = 100\ \ \text{ and}\ \ \ D = 375\)

\(T\) \(=\dfrac{375}{100}\)
  \(=3.75\ \text{hours}\)
  \(=3\ \text{hrs}\ \ 45\ \text{minutes}\)

  
\(\Rightarrow C\)

v1 Algebra, STD2 A1 2011 HSC 21 MC

A train departs from Town A at 4.00 pm to travel to Town B. Its average speed for the journey is 80 km/h, and it arrives at 6.00 pm. A second train departs from Town A at 4.30 pm and arrives at Town B at 6.10 pm.

What is the average speed of the second train?

  1. 96 km/h
  2. 114 km/h
  3. 224 km/h
  4. 280 km/h
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\(A\)

Show Worked Solution

\(\text{1st train:}\)

\(\text{Travels 2hrs at 80km/h}\)

\(\text{Distance}\) \(=\text{Speed}\times\text{Time}\)
  \(=80\times 2\)
  \(=160\ \text{km}\)

 
\(\text{2nd train:}\)

\(\text{Travels 160 km in 1 hr 40 min}\ \rightarrow\ \dfrac{5}{3}\ \text{hrs}\)

\(\text{Speed}\) \(=\dfrac{\text{Distance}}{\text{Time}}\)
  \(=160\ ÷\ \dfrac{5}{3}\)
  \(=160\times \dfrac{3}{5}\)
  \(=96\ \text{km/h}\)

\(\Rightarrow A\)


♦♦ Mean mark 49%.

v1 Algebra, STD2 A1 2009 HSC 16 MC

The time for a train to travel a certain distance varies inversely with its speed.

Which of the following graphs shows this relationship?

   

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\(C\)

Show Worked Solution
\(T\) \(\propto \dfrac{1}{S}\)
\(T\) \(=\dfrac{k}{S}\)

 
\(\text{By elimination:}\)

\(\text{As   Speed} \uparrow \ \text{, Time}\downarrow\ \Rightarrow\ \text{cannot be A or B}\)

\(\text{D  is incorrect because it graphs a linear relationship}\)

\(\Rightarrow C\)


♦♦ Mean mark 38%.

v1 Algebra, STD2 A1 SM-Bank 2 MC

Frank lives 45 kilometres from his work.

On Monday, he drove to work and averaged 60 kilometres per hour.

On Wednesday, he took the train which averaged 90 kilometres per hour.

What was the extra time of the car journey on Monday, in minutes, compared to when he caught the train on Wednesday?

  1.  15
  2.  30
  3.  45
  4.  75
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\(A\)

Show Worked Solution

\(\text{Time}=\dfrac{\text{distance}}{\text{speed}}\)
  

\(\text{Time on Monday}\) \(=\dfrac{45}{60}\)
  \(=0.75\ \text{hour}\)
  \(=45\ \text{minutes}\)

 

\(\text{Time on Wednesday}\) \(=\dfrac{45}{90}\)
  \(=0.5\ \text{hour}\)
  \(=30\ \text{minutes}\)

 

\(\therefore\ \text{The extra time driving the car}=45-30=15\ \text{minutes}\)
 

\(\Rightarrow A\)

v1 Algebra, STD2 A1 SM-Bank 15

Alonso drove 400 km in \(5\frac{1}{2}\) hours.

His average speed for the first 240 km was 80 km per hour.

How long did he take to travel the last 160 km?  (2 marks)

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\(2\frac{1}{2}\ \text{hours}\)

Show Worked Solution

\(\text{Time for 1st 240 km}\)

\(=\dfrac{240}{80}\)

\(= 3\ \text{hours}\)

 

\(\therefore\ \text{Time for last 160 km}\)

\(=5\frac{1}{2}-3\)

\(=2\frac{1}{2}\ \text{hours}\)

v1 Algebra, STD2 A1 2020 HSC 3 MC

The distance between the Yarra Valley and Ballarat is 150 km. A person travels from the Yarra Valley to Ballarat at an average speed of 90 km/h.

How long does it take the person to complete the journey?

  1.  60 minutes
  2.  66 minutes
  3.  1 hour 30 minutes
  4.  1 hour 40 minutes
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\(D\)

Show Worked Solution
\(\text{Time}\) \(=\dfrac{\text{Distance}}{\text{Speed}}\)
  \(=\dfrac{150}{90}\)
  \(=1.\dot{6}\ \text{hours}\)
  \(=1\ \text{hour}\ 40\ \text{minutes}\)

 
\(\Rightarrow D\)