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Measurement, STD2 EQ-Bank 25

A bus departs Sydney at 8:00 am on Monday for Perth. The bus makes five stops on the journey whose durations are given below: 

  • Dubbo: 45 minutes
  • Broken Hill: 1 hour 15 minutes
  • Port Augusta: 50 minutes
  • Ceduna: 40 minutes
  • Norseman: 1 hour 10 minutes

The total driving time (excluding stops) is 52 hours and 30 minutes. The bus arrives in Perth at 3:25 pm on Thursday.

  1. Calculate the total time for the journey from Sydney to Perth, including all stops. Give your answer in hours and minutes.   (2 marks)
  2. Convert your answer from part (a) to days, hours and minutes, and hence state the day and time the bus arrives in Perth. Ignore time zones in your calculations.   (2 marks)
Show Answers Only

a.   \(\text{57 hours 10 minutes}\)

b.   \(\text{Bus arrives on Wednesday at 5:10 pm with the journey}\)

\(\text{taking 2 days 9 hours 10 minutes.}\)

Show Worked Solution

a.   \(\text{Total stopping time}\)

\(=45+75+50+40+70\)

\(= 280 \text{ minutes}= 4\ \text{hours}\ 40 \text{ minutes} \)

\(\text{Total journey}\)

\(=52\ \text{hours}\ 30 \text{ minutes}+4\ \text{hours}\ 40 \text{ minutes} \)

\(=57\ \text{hours}\ 10 \text{ minutes} \)
  

b.   \(\text{Convert 57 hours 10 minutes to days, hours and minutes:}\)

\(57\ \text{hours}=(2 \times 24) + 9=2\ \text{days}\ 9\ \text{hours}\)

\(57\ \text{ hours 10 minutes}=2\ \text{days}\ 9\ \text{hours}\ 10\ \text{minutes}\)
 

\(\text{Bus arrival in Perth:}\)

\(\rightarrow\ \text{Bus departs 8 am Monday}\)

\(\rightarrow\ \text{Monday 8:00 am + 2 days = Wednesday 8:00 am}\)

\(\rightarrow\ \text{Wednesday 8:00 am + 9 hours 10 minutes = Wednesday 5:10 pm}\)

\(\therefore\ \text{Bus arrives Wednesday at 5:10 pm.}\)

Measurement, STD2 EQ-Bank 21

A concert runs for 5400 seconds.

  1. Convert this time to hours and minutes.   (2 marks)
  2. If the concert finishes at 10:45 pm, what time did it start?   (2 marks)
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a.   \(\text{1 hours 30 minutes}\)

b.   \(\text{9:15 pm}\)

Show Worked Solution

a.   \(\text{Step 1: Convert seconds to minutes}\)

\(5400 \text{ seconds} = \dfrac{5400}{60} \text{ minutes} = 90 \text{ minutes} \)

\(\text{Step 2: Convert minutes to hours and minutes}\)

\(90 \text{ minutes} = \dfrac{90}{60} \text{ hours} = 1.5 \text{ hours} \)

\(\therefore\ 90 \text{ minutes} = 1 \text{ hour } 30 \text{ minutes} \)
  

b.   \(\text{Finish time: 10:45 pm}\)

\(\text{Concert duration: 1 hours 30 minutes}\)

\(10:45\ \text{pm}-1\ \text{hour}=9:45\ \text{pm}\)

\(9:45\ \text{pm}-30\ \text{minutes}=9:15\ \text{pm}\)

\(\text{Start time: 9:15 pm}\)

Measurement, STD2 EQ-Bank 20

A movie runs for 8400 seconds.

  1. Convert this time to hours and minutes.   (2 marks)
  2. If the movie starts at 7:15 pm, what time will it finish?   (1 mark)
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a.   \(\text{2 hours 20 minutes}\)

b.   \(\text{9:35 pm}\)

Show Worked Solution

a.   \(\text{Step 1: Convert seconds to minutes}\)

\(8400 \text{ seconds} = \dfrac{8400}{60} \text{ minutes} = 140 \text{ minutes} \)

\(\text{Step 2: Convert minutes to hours and minutes}\)

\(140 \text{ minutes} = \dfrac{140}{60} \text{ hours} = 2.333… \text{ hours} \)

\(\text{To find the minutes part:}\ 140 = 2 \times 60 + 20  \)

\(\therefore\ 140 \text{ minutes} = 2 \text{ hours } 20 \text{ minutes} \)
  

b.   \(\text{Starting time: 7:15 pm}\)

\(\text{Movie duration: 2 hours 20 minutes}\)

\(\text{Finish time: 9:35 pm}\)

Measurement, STD2 EQ-Bank 8 MC

Convert 10 500 seconds to hours and minutes.

  1. 2 hours 55 minutes
  2. 3 hours 15 minutes
  3. 2 hours 50 minutes
  4. 175 minutes
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\(A\)

Show Worked Solution

\(\text{Convert seconds to minutes:}\)

\(10\,500 \text{ seconds} = \dfrac{10\,000}{60} \text{ minutes} = 175 \text{ minutes} \)
 

\(\text{Convert minutes to hours and minutes:}\)

\(175 \text{ minutes} = \dfrac{175}{60} \text{ hours} = 2.916… \text{ hours} \)
 

\(\text{Calculate minutes:}\ 175-2 \times 60=55  \)

\(\therefore\ 175 \text{ minutes} = 2 \text{ hours } 55 \text{ minutes} \)

\(\Rightarrow A\)

Measurement, STD2 EQ-Bank 6 MC

Jeremy watched a movie at the cinema that began at 11:35 am. If it finished at 2:05 pm, what was the duration of the movie, in minutes?

  1. 25 minutes
  2. 125 minutes
  3. 150 minutes
  4. 250 minutes
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\(C\)

Show Worked Solution

\(\text{11:35 to 2:05 = 2.5 hours}\)

\(\text{To convert hours to minutes multiply by 60.}\)

\( 2.5 \text{ hours} = 2.5 \times 60 \text{ minutes} = 150 \text{ minutes} \)

\(\Rightarrow C\)