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Geometry, NAP-B4-CA22

 
The distance on the map from Hill End to Rouse Hill along the road is 5 cm.

How long will it take to walk from Hill End to Rouse Hill along the road at a speed of 6 kilometres per hour?

 
 1 hour 15 minutes
 
 1 hour 25 minutes
 
 12 hours 5 minutes
 
 12 hours 30 minutes
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`text(1 hour 15 minutes)`

Show Worked Solution
`text(Distance)` `= 5 xx 1500`
  `= 7500\ text(m)`
  `= 7.5\ text(km)`

 

`:.\ text(Walk Time)` `= 7.5/6`
  `= 1.25\ text(hours)`
  `= 1\ text(hour 15 minutes)`

Number, NAP-D4-NC31 SA

A greyhound runs a 1500 metre race.

The time it takes for each 500 metres is recorded in the table below.
 

 
What was the average speed of the greyhound over the full 1500 metre race, in metres per second?

  metres per second
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`25\ \ text(metres per second)`

Show Worked Solution

`text(Total seconds to complete the race)`

`=23 + 19 +18`

`=60`

`:.\ text(Average speed)` `=1500/60`
  `=150/6`
  `=25\ \ text(metres per second)`

Number, NAP-E4-CA06

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?

`15` `45` `60` `75`
 
 
 
 
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`45\ text(minutes)`

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)`

Number, NAP-F4-CA14

Lachlan drives his boat to an island 100 km away at an average speed of 80 km/h.

How long does the trip take?

`text(48 minutes)` `text(1 hour 15 minutes)` `text(1 hour 20 minutes)` `text(1 hour 30 minutes)`
 
 
 
 
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`text(1 hour 15 minutes)`

Show Worked Solution
`text(Time)` `= text(Distance)/text(Speed)`
  `= 100/80`
  `= 1.25\ text(hours)`
  `=1\ text(hour 15 minutes)`

Number, NAP-G4-NC32 SA

Joe is in a 2-day rally car race.

On day 1, Joe takes 1 hour and 15 minutes to travel 105 km.

On day 2, Joe takes 1 hour and 30 minutes to travel 225 km.

What is Joe's average speed over the 2 days.

  kilometres per hour
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`120\ text(km/h)`

Show Worked Solution

`1 1/4\ text(hours → 105 km)`

`1 1/2\ text(hours → 225 km)`

`2 3/4\ text(hours → 330 km)`
 

`:.\ text(Average speed)` `= text(Distance)/text(Time)`
  `= 330/(11/4)`
  `= 330 xx 4/11`
  `= 120\ text(km/h)`

Number, NAP-H4-NC11

 

 
Which of the following situations best fits the distance/time graph above?

 
 Matt ran to the park, sat down on a bench, and then walked home.
 
 Matt walked to the park, sat down on a bench, and walked back home.
 
 Matt walked to the park, sat down on a bench and ran home.
 
 Matt walked to the park and back home without stopping. 
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`text(Matt walked to the park, sat down on)`

`text(a bench and ran home.)`

Show Worked Solution

`text(Matt walked to the park, sat down on)`

STRATEGY: The steep line returning home shows he travelled faster than getting there.

`text(a bench and ran home.)`

Number, NAP-H4-CA05

A bullet fired from a hand gun travels at 390 metres per second.

What is the speed of the bullet in metres per minute?

`39\ 000`    `23\ 400`    `6.5`      `3.9`  
 
 
 
 
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`23\ 400\ text(metres per minute)`

Show Worked Solution
`text(Speed)` `= (390 xx 60)`
  `= 23\ 400\ \ \ text(metres per minute)`