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Algebra, STD2 A1 2024 HSC 11 MC

A train left Richmond at 6:42 am and arrived at Central Station at 8:04 am. The distance travelled by the train from Richmond to Central was 61 km.

What was the average speed of this train, correct to the nearest km/h ?

  1. 38
  2. 45
  3. 50
  4. 74
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\(B\)

Show Worked Solution

\(\text {Time of travel:  8:04 less 6:42 = 82 minutes.}\)

  \(\text{Speed (avg)}\) \(=\dfrac{\text{distance}}{\text{time}}\)
    \(=\dfrac{61}{82}\ \ \text{km/min}\)
    \(=\dfrac{61}{82} \times 60\ \ \text{km/hr}\)
    \(=44.6\ \ \text{km/hr}\)

 
\(\Rightarrow B\)

Measurement, STD1 M4 2023 HSC 14

The distance-time graph shows the first two stages of a car journey from home to a holiday house.
  

  1. At what speed, in kilometres per hour, did the car travel during stage \(A\) of the journey?   (1 mark)

  2. For how long did the car stop during stage \(B\) of the journey?   (1 mark)

  3. After stage \(B\), the car continues to travel towards the holiday house at a constant speed of \(50\ \text{km/h}\) for 2 hours. Graph this part of the journey on the grid above.   (2 marks)

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a.    \(100\text{ km/h}\)

b.    \(30\text{ minutes}\)

c.   

Show Worked Solution

a.   \(S=\dfrac{D}{T}=\dfrac{150}{1.5}=100\ \text{km/h}\)
 

b.    \(\text{Stage}\textit{ B}=1.5\rightarrow 2\text{ hours}=30\text{ minutes}\)
 

c.    \(\text{Position after 2 hours at 50km/h}=(150+2\times 50 , 2 + 2) = (250 , 4)\)


♦ Mean mark (c) 50%.

Algebra, STD2 A1 2020 HSC 3 MC

The distance between Bricktown and Koala Creek is 75 km. A person travels from Bricktown to Koala Creek at an average speed of 50 km/h.

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

  1.  40 minutes
  2.  1 hour 25 minutes
  3.  1 hour 30 minutes
  4.  1 hour 50 minutes
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`C`

Show Worked Solution
`text(Time)` `= frac(text(Distance))(text(Speed))`
  `= frac(75)(50)`
  `=1.5 \ text(hours)`
  `= 1 \ text(hour) \ 30 \ text(minutes)`

 
`=> \ C`

Algebra, STD2 A1 SM-Bank 15

Fabio drove 300 km in  `4 1/2`  hours.

His average speed for the first 210 km was 70 km per hour.

How long did he take to travel the last 90 km?  (2 marks)

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`1 1/2`

Show Worked Solution

`text(Time for 1st 210 km)`

`= 210/70`

`= 3\ text(hours)`

 

`:.\ text(Time for last 90 km)`

`= 4 1/2 – 3`

`= 1 1/2\ text(hours)`

Algebra, STD2 A1 SM-Bank 2 MC

Fleur lives 15 kilometres from her work.

On Wednesday, she drove to work and averaged 60 kilometres per hour.

On Thursday, she took the bus which averaged 15 kilometres per hour.

What was the extra time of the bus journey, in minutes, compared to when she drove on Wednesday?

  1.  15
  2.  45
  3.  60
  4.  75
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`B`

Show Worked Solution
`text(Time on Wednesday)` `= 15/60`
  `= 0.25\ text(hour)`
  `= 15\ text(minutes)`

 

`text(Time on Thursday)` `= 15/15`
  `= 1\ text(hour)`
  `= 60\ text(minutes)`

 

`:.\ text(The extra time taking the bus)\ =60-15 = 45\ text(minutes)`

`=>B`

Algebra, STD2 A1 2017 HSC 2 MC

A car is travelling at 95 km/h.

How far will it travel in 2 hours and 30 minutes?

A.     `38\ text(km)`

B.     `41.3\ text(km)`

C.     `218.5\ text(km)`

D.     `237.5\ text(km)`

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`text(D)`

Show Worked Solution
`text(Distance)` `= 95 xx 2.5`
  `= 237.5\ text(km)`

`=>\ text(D)`

Algebra, STD2 A1 2009 HSC 16 MC

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

Which of the following graphs shows this relationship?
 

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`A`

Show Worked Solution
`T` `prop 1/S`
`T` `= k/S`

 
`text{By elimination:}`

`text(As   S) uarr text(, T) darr => text(cannot be B or D)`

♦ Mean mark 38%

`text(C  is incorrect because it graphs a linear relationship)`

`=>  A`

Algebra, STD2 A1 2011 HSC 21 MC

A train departs from Town A at 3.00 pm to travel to Town B. Its average speed for the
journey is 90 km/h, and it arrives at 5.00 pm. A second train departs from Town A at
3.10 pm and arrives at Town B at 4.30 pm.

What is the average speed of the second train?

  1.   135 km/h
  2. 150 km/h
  3.   216 km/h
  4.   240 km/h
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`A`

Show Worked Solution

 `text(1st train)`

♦ Mean mark 49%

`text(Travels 2hrs at 90km/h)`

`text(Distance)` `=text(Speed)xxtext(Time)`
  `=90xx2`
  `=180\ text(km)`

 
`text(2nd train)`

`text(Travels 180 km in 1 hr 20 min)\ (4/3\ text(hrs))`

`text(Speed)` `=text(Distance)/text(Time)`
  `=180-:4/3`
  `=180xx3/4`
  `=135\ text(km/h)`

`=> A`

Algebra, STD2 A1 2012 HSC 15 MC

A car takes 6 hours to complete a journey when travelling at 60 km/h.

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

  1.    36 minutes
  2.      1 hour and 40 minutes
  3.      3 hours and 6 minutes
  4.      3 hours and 36 minutes
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`D`

Show Worked Solution

`T = D/S`

`text(S)text(ince)\ \ \ T = 6\ \ \ text(when)\ \ \ S = 60`

`6` `= D/60`
`D` `= 360\ text(km)`

 

`text(Find)\ \ T\ \ text (when)\ \ \ S = 100\ \ text(and)\ \ \ D = 360`

`T` `= 360/100`
  `= 3.6\ text(hours)`
  `= 3\ text(hrs)\ \ 36\ text(minutes)`

`=>  D`