20180

Question

{{{question}}}

Worked Solution

{{{workedSolution}}}

Variant 0

DifficultyLevel

655

Question

Pat, Mitch and Josh entered a long distance relay race as a team.

They divided the total distance into 20 equal sections.

Pat ran 920\dfrac{9}{20} of the total distance.

Mitch ran 320\dfrac{3}{20} more of the total distance than Josh.

What fraction of the total distance did Josh run?

Worked Solution

Total distance Mitch and Josh run = 1 −- 920\dfrac{9}{20} = 1120\dfrac{11}{20}

⇒\rArr Mitch runs = 720\dfrac{7}{20}

⇒\rArr Josh runs = 420\dfrac{4}{20}

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
Pat, Mitch and Josh entered a long distance relay race as a team. They divided the total distance into 20 equal sections. Pat ran $\dfrac{9}{20}$ of the total distance. Mitch ran $\dfrac{3}{20}$ more of the total distance than Josh. What fraction of the total distance did Josh run?
workedSolution
Total distance Mitch and Josh run = 1 $-$ $\dfrac{9}{20}$ = $\dfrac{11}{20}$ $\rArr$ Mitch runs = $\dfrac{7}{20}$ $\rArr$ Josh runs = {{{correctAnswer}}}
correctAnswer
$\dfrac{4}{20}$

Answers

Is Correct?Answer
✓

420\dfrac{4}{20}

x

720\dfrac{7}{20}

x

820\dfrac{8}{20}

x

1720\dfrac{17}{20}

Variant 1

DifficultyLevel

653

Question

Jenny, Karen and Leanne entered a long distance walk for charity as a team.

They divided the total distance into 30 equal sections.

Jenny walked 1330\dfrac{13}{30} of the total distance.

Karen walked 730\dfrac{7}{30} more of the total distance than Leanne.

What fraction of the total distance did Leanne walk?

Worked Solution

Total distance Karen and Leanne walk = 1 −- 1330\dfrac{13}{30} = 1730\dfrac{17}{30}

⇒\rArr Karen walks = 1230\dfrac{12}{30}

⇒\rArr Leanne walks = 530\dfrac{5}{30}

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
Jenny, Karen and Leanne entered a long distance walk for charity as a team. They divided the total distance into 30 equal sections. Jenny walked $\dfrac{13}{30}$ of the total distance. Karen walked $\dfrac{7}{30}$ more of the total distance than Leanne. What fraction of the total distance did Leanne walk?
workedSolution
Total distance Karen and Leanne walk = 1 $-$ $\dfrac{13}{30}$ = $\dfrac{17}{30}$ $\rArr$ Karen walks = $\dfrac{12}{30}$ $\rArr$ Leanne walks = {{{correctAnswer}}}
correctAnswer
$\dfrac{5}{30}$

Answers

Is Correct?Answer
x

2330\dfrac{23}{30}

x

1230\dfrac{12}{30}

✓

530\dfrac{5}{30}

x

1730\dfrac{17}{30}

Variant 2

DifficultyLevel

665

Question

A walking trail consists of bush walking, beach walking and a steep hill climb through a park.

The walking trail is divided into 25 equal sections.

The bush walk makes up 1425\dfrac{14}{25} of the total walking trail.

The beach walk makes up 15\dfrac{1}{5} more of the total walking trail than the hill climb.

What fraction of the total trail is the hill climb?

Worked Solution

Combined distance of the beach walk and hill climb = 1 −- 1425\dfrac{14}{25} = 1125\dfrac{11}{25}

⇒\rArr Beach walk = 825\dfrac{8}{25}

⇒\rArr Hill climb = 325\dfrac{3}{25}

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
A walking trail consists of bush walking, beach walking and a steep hill climb through a park. The walking trail is divided into 25 equal sections. The bush walk makes up $\dfrac{14}{25}$ of the total walking trail. The beach walk makes up $\dfrac{1}{5}$ more of the total walking trail than the hill climb. What fraction of the total trail is the hill climb?
workedSolution
Combined distance of the beach walk and hill climb = 1 $-$ $\dfrac{14}{25}$ = $\dfrac{11}{25}$ $\rArr$ Beach walk = $\dfrac{8}{25}$ $\rArr$ Hill climb = {{{correctAnswer}}}
correctAnswer
$\dfrac{3}{25}$

Answers

Is Correct?Answer
x

1125\dfrac{11}{25}

x

725\dfrac{7}{25}

x

525\dfrac{5}{25}

✓

325\dfrac{3}{25}

Variant 3

DifficultyLevel

651

Question

Jo, Nat and Alex entered a lake swim relay as a team.

They divided the total distance into 20 equal sections.

Jo swam 320\dfrac{3}{20} of the total distance.

Nat swam 320\dfrac{3}{20} more of the total distance than Alex.

What fraction of the total distance did Alex swim?

Worked Solution

Total distance Nat and Alex swim = 1 −- 320\dfrac{3}{20} = 1720\dfrac{17}{20}

⇒\rArr Nat swims = 1020\dfrac{10}{20}

⇒\rArr Alex swims = 720\dfrac{7}{20}

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
Jo, Nat and Alex entered a lake swim relay as a team. They divided the total distance into 20 equal sections. Jo swam $\dfrac{3}{20}$ of the total distance. Nat swam $\dfrac{3}{20}$ more of the total distance than Alex. What fraction of the total distance did Alex swim?
workedSolution
Total distance Nat and Alex swim = 1 $-$ $\dfrac{3}{20}$ = $\dfrac{17}{20}$ $\rArr$ Nat swims = $\dfrac{10}{20}$ $\rArr$ Alex swims = {{{correctAnswer}}}
correctAnswer
$\dfrac{7}{20}$

Answers

Is Correct?Answer
x

620\dfrac{6}{20}

✓

720\dfrac{7}{20}

x

1020\dfrac{10}{20}

x

1720\dfrac{17}{20}

Variant 4

DifficultyLevel

653

Question

Year 9 Art classes are tiling a mural in the canteen using orange, red and black tiles.

They divided the total area into 50 equal sections.

Orange tiles make up 1750\dfrac{17}{50} of the total area.

Black tiles make up 550\dfrac{5}{50} more of the total area than red.

What fraction of the total area is made up of red tiles?

Worked Solution

Total area made up of black and red tiles = 1 −- 1750\dfrac{17}{50} = 3350\dfrac{33}{50}

⇒\rArr Black tiles = 1920\dfrac{19}{20}

⇒\rArr Red tiles = 1450\dfrac{14}{50}

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
Year 9 Art classes are tiling a mural in the canteen using orange, red and black tiles. They divided the total area into 50 equal sections. Orange tiles make up $\dfrac{17}{50}$ of the total area. Black tiles make up $\dfrac{5}{50}$ more of the total area than red. What fraction of the total area is made up of red tiles?
workedSolution
Total area made up of black and red tiles = 1 $-$ $\dfrac{17}{50}$ = $\dfrac{33}{50}$ $\rArr$ Black tiles = $\dfrac{19}{20}$ $\rArr$ Red tiles = {{{correctAnswer}}}
correctAnswer
$\dfrac{14}{50}$

Answers

Is Correct?Answer
✓

1450\dfrac{14}{50}

x

1250\dfrac{12}{50}

x

3350\dfrac{33}{50}

x

2250\dfrac{22}{50}

Tags