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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 23

Day 1 of the Ashes Test match at the SCG begins at 10:30 am. Each session of play lasts 2 hours, with a 40-minute lunch break after the first session and a 20-minute tea break after the second session. Rain delays the start of the third session by 37 minutes.

At what time does play finish for Day 1?   (2 marks)

Show Answers Only

\(6:07\ \text{pm}\)

Show Worked Solution

\(\text{Total time }\)

\(=2\ \text{hours}\times 3+40\ \text{minutes}+20\ \text{minutes}+37\ \text{minutes}\)

\(=7\ \text{hours}\ 37\ \text{ minutes}\)

\(\text{Since match starts at }10:30\ \text{am}:\)

\(\text{Finish time}=10:30\ \text{am}+7\ \text{hours}\ 37\ \text{ minutes}=6:07\ \text{pm}\)

Measurement, STD2 EQ-Bank 27

A basketball game starts at 6:35 pm. The game consists of four quarters that are 10 minutes each, with a 2-minute break after the first and third quarters and an 8-minute break at half time.

  1. The home team scores a three-pointer 6 minutes into the second quarter. At what time does this occur?   (2 marks)
  2. If 4 minutes injury time is added to the total time, at what time does the game finish?   (2 marks)
Show Answers Only

a.   \(6:53\ \text{pm}\)

b.   \(7:31\ \text{pm}\)

Show Worked Solution

a.   \(\text{Match starts at }6:35\ \text{pm}\)

\(\text{Calculate time elapsed until 6 minutes into the second quarter:}\)

\(\text{Total time before three-pointer}\)

\(=10+2+6=18\text{ minutes}\)

\(\therefore\ \text{Three pointer is scored at: }6:35+18\ \text{minutes}=6:53\ \text{pm}\)
 

b.   \(\text{Total duration of game}\)

\(=4 \times 10+2 \times 2+8+4=56\ \text{minutes}\)

\(\therefore\ \text{Finish time}=6:35+56\ \text{minutes}=7:31\ \text{pm}\)

Measurement, STD2 EQ-Bank 24

Sarah's netball match starts at 1:45 pm. The match consists of four quarters that are 12 minutes each, with a 3-minute break after the first and third quarters, and a 7-minute break at half time.

  1. Sarah intercepts the ball 8 minutes into the third quarter. At what time does this occur?   (2 marks)
  2. At what time does the match finish?   (2 marks)
Show Answers Only

a.   \(2:27\ \text{pm}\)

b.   \(2:46\ \text{pm}\)

Show Worked Solution

a.   \(\text{Match starts at }1:45\ \text{pm}\)

\(\text{Calculate time elapsed until 8 minutes into the third quarter:}\)

\(\text{Total time before intercept}\)

\(=12+3+12+7+8=42\text{ minutes}\)

\(\therefore\ \text{Sarah intercepts the ball at: }1:45+42\ \text{minutes}=2:27\ \text{pm}\)
 

b.   \(\text{Total duration of game}\)

\(=4 \times 12+2 \times 3+7=61\ \text{minutes}\)

\(\therefore\ \text{Finish time}=1:45+61\ \text{minutes}=2:46\ \text{pm}\)

Measurement, STD2 EQ-Bank 26

Use the train timetable below to answer this question.

Emma lives in Berowra and travels to Wyong for an appointment. After her appointment, she needs to attend a meeting in Gosford before returning home to Berowra.

  1. Emma catches the train that departs Wyong at 09:16. How long does this train take to reach Gosford?   (1 mark)
  2. Emma's meeting in Gosford starts at 10:15 am at a venue that is 7 minutes walk from Gosford station. What is the latest train she can catch from Wyong to arrive at her meeting on time?   (2 marks)
  3. After her meeting finishes at 11:20 am, Emma walks back to Gosford station (taking 7 minutes). What is the earliest train she can catch from Gosford to return home to Berowra, and what time will she arrive home?   (2 marks)
Show Answers Only

a.   \(17\ \text{minutes}\)

b.   \(09:37\ \text{train}\)

c.   \(\text{11:34 am Gosford train, arrives at Berowra at 12:37 pm}\)

Show Worked Solution

a.   \(\text{Elapsed time:}\ =09:33-09:16 = 17 \text{ minutes} \)

b.   \(\text{Step 1: Meeting starts at 10:15 am}\)

\(\rightarrow\ 7\text{ minutes to walk from Gosford station to the venue.}\)

\(\rightarrow\ \text{At Gosford Station by: }\ 10:15-7 \text{ minutes} = 10:08 \text{ am}\)

\(\text{Step 2: Find latest train arriving at Gosford by 10:08 am}\)

\(\rightarrow\ \text{Arrival times: } 08:12, 08:33, 08:58, 09:33, 09:58, 10:33\)

\(\rightarrow\ \text{She must catch the }09:58.\)

\(\text{Step 3: When does 09:58 depart Wyong?}\)

\(\rightarrow\ 09:37\ \text{train}\)

c.   \(\text{Step 1: Determine when Emma arrives back at Gosford station}\)

\(\rightarrow\ \text{Meeting finishes at }11:20 \text{ am}\)

\(\text{Walking time back to station: 7 minutes}\)

\(\text{Emma arrives at Gosford station at:}\ 11:20 + 7 \text{ minutes} = 11:27 \text{ am} \)

\(\text{Step 1: Find the earliest train departing Gosford after 11:27 am}\)

\(\rightarrow\ \text{Meeting finishes at }11:20 \text{ am}\)

\(\rightarrow\ \text{Relevant departure times:} …10:34, 10:59, 11:34, 11:59\)

\(\rightarrow\ \text{Earliest train after 11:27 am is the }11:34 \text{ am}\)

\(\text{Step 3: Find when this train arrives in Berowra}\)

\(\rightarrow\ \text{11:34 am Gosford train, arrives at Berowra at }12:37 \text{ pm}\)

Measurement, STD2 EQ-Bank 14 MC

Use the bus timetable below to answer this question.

John works weekend shifts at a cafe near Hornsby station. He needs to be at work by 9:30 am.

It takes him 12 minutes to walk from his home to Pennant Hills Station and 8 minutes to walk from Hornsby Station to his workplace.

What is the latest bus he can catch from Pennant Hills Station and what time must he leave home? 

  1. 8:40 bus, leaving home at 8:28
  2. 9:00 bus, leaving home at 8:48
  3. 9:20 bus, leaving home at 9:08
  4. 9:40 bus, leaving home at 9:28
Show Answers Only

\(B\)

Show Worked Solution

\(\text{Work backwards from when John needs to be at work.}\)

\(\text{John must arrive at work by 9:30 am:}\)

\(\rightarrow\ 8\text{ minutes to walk from Hornsby Station to work.}\)

\(\rightarrow\ \text{Must arrive at Hornsby Station by: }\ 9:30-8 \text{ minutes} = 9:22 \text{ am}\)
 

\(\text{Find the latest bus arriving at Hornsby Station by 9:22 am:}\)

\(\rightarrow\ \text{Arrival times: } 08:37, 08:57, 09:17, 09:37…\)

\(\rightarrow\ \text{He must catch the }09:17.\)

\(\rightarrow\ 09:17\ \text{departs Pennant Hills Station at }09:00.\)
  

\(\text{John needs to leave home 12 minutes before train comes:}\)

\(\rightarrow\ 9:00-12 \text{ minutes} = 8:48 \text{ am} \)
   

\(\Rightarrow B\)

Measurement, STD2 EQ-Bank 7 MC

On Tuesday Sarah started work at 6:45 am and finished at 3:12 pm.

For how many hours and minutes did Sarah work on Tuesday?

  1. 8 hours 27 minutes
  2. 8 hours 33 minutes
  3. 9 hours 27 minutes
  4. 9 hours 33 minutes
Show Answers Only

\(A\)

Show Worked Solution

\(\text{Break into steps}\)

\(\text{From 6:45 am to 7:00 am: }\ 60-45 = 15 \text{ minutes} \)

\(\text{From 7:00 am to 3:12 pm: }\  8\ \text{hours}\ 12 \text{ minutes} \)

\(\text{Total: }\  8\ \text{hours}+12 \text{ minutes} +15 \text{ minutes}=8\ \text{hours}\ 27\ \text{minutes}\)

\(\Rightarrow A\)

Measurement, STD2 EQ-Bank 5 MC

A bus departs at 8:23 am and arrives at its destination at 11:47 am.

How long was the bus journey?

  1. 3 hours 24 minutes
  2. 3 hours 34 minutes
  3. 4 hours 24 minutes
  4. 4 hours 34 minutes
Show Answers Only

\(A\)

Show Worked Solution

\(\text{Method 1: Break into steps}\)

\(\rightarrow\text{From 8:23 am to 9:00 am: }\ 60-23 = 37 \text{ minutes} \)

\(\rightarrow\text{From 9:00 am to 11:47 am: }\  2\ \text{hours}\ 47 \text{ minutes} \)

\(\rightarrow\text{Total: }\  37 \text{ minutes} + 2\ \text{hours}+\ 47 \text{ minutes}=2\ \text{hours}\ 84\ \text{minutes}\)

\(=3\ \text{hours}\ 24\ \text{minutes}\)
  

\(\text{Method 2: Calculate hours and minutes separately}\)

\(\rightarrow\text{Hours: } \ 11-8 = 3 \text{ hours} \)

\(\rightarrow\text{Minutes: }\ 47-23 = 24 \text{ minutes} \)

\(\rightarrow\text{Total: }\ 3 \text{ hours } 24 \text{ minutes} \)
  

\(\Rightarrow B\)

Measurement, STD2 EQ-Bank 3 MC

It is currently 2:17 pm. A train is due to arrive at 3:08 pm.

How long do you need to wait for the train?

  1. 49 minutes
  2. 51 minutes
  3. 1 hour 9 minutes
  4. 1 hour 51 minutes
Show Answers Only

\(B\)

Show Worked Solution

\(\text{Method 1: Break into steps}\)

\(\rightarrow\text{From 2:17 pm to 3:00 pm: }\ 60-17 = 43 \text{ minutes} \)

\(\rightarrow\text{From 3:00 pm to 3:08 pm: }\  8 \text{ minutes} \)

\(\rightarrow\text{Total: }\  43+8 = 51 \text{ minutes} \)
  
\(\text{Method 2: Calculate directly}\)

\(\rightarrow 3:08-2:17 = 51 \text{ minutes} \)
  

\(\Rightarrow B\)

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)
Show Answers Only

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)
Show Answers Only

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.   \(\text{Starting time: 7:15 pm}\)

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

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