Question

Alex and Sam also build tables.
Together they make 10 tables in 12 days.
Alex working alone can make 10 in 30 days.
How long would it take Sam working alone to make 10 tables?

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Best answer will mark and verify :

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Answer 1

$\mathfrak\blue{Question}$

Alex and Sam also build tables.

Together they make 10 tables in 12 days.

Alex working alone can make 10 in 30 days.

How long would it take Sam working alone to make 10 tables?

$\huge\mathtt\red{Solution}$

$Turn \: the \: English \: into \: Algebra\: -$

Letters:

Use a for Alex's work rate

Use s for Sam's work rate

12 days of Alex and Sam is 10 tables -

so: 12a + 12s = 10

30 days of Alex alone is also 10 tables: 30a = 10

We are being asked how long it would take Sam to make 10 tables.

$\mathbf\green{To \: slove \: -}$

• 30a = 10, so Alex's rate (tables per day) is -
• a = 10/30 = 1/3

• Start with: 12a + 12s = 10
• Put "1/3" for a: 12(1/3) + 12s = 10
• Simplify: 4 + 12s = 10
• Subtract 4 from both sides: 12s = 6
• Divide both sides by 12: s = 6/12
• Simplify: s = 1/2

Which means that Sam's rate is half a table a day (faster than Alex!)

So 10 tables would take Sam just 20 days.

Hope it's helpful for you.

Answer 2

Answer:

Alex and Sam also build tables.

Together they make 10 tables in 12 days.

Alex working alone can make 10 in 30 days.

How long would it take Sam working alone to make 10 tables?

\huge\mathtt\red{Solution}Solution

Turn \: the \: English \: into \: Algebra\: -TurntheEnglishintoAlgebra−

Letters:

Use a for Alex's work rate

Use s for Sam's work rate

12 days of Alex and Sam is 10 tables -

so: 12a + 12s = 10

30 days of Alex alone is also 10 tables: 30a = 10

We are being asked how long it would take Sam to make 10 tables.

\mathbf\green{To \: slove \: -}Toslove−

30a = 10, so Alex's rate (tables per day) is -

a = 10/30 = 1/3

Start with: 12a + 12s = 10

Put "1/3" for a: 12(1/3) + 12s = 10

Simplify: 4 + 12s = 10

Subtract 4 from both sides: 12s = 6

Divide both sides by 12: s = 6/12

Simplify: s = 1/2

Which means that Sam's rate is half a table a day (faster than Alex!)

So 10 tables would take Sam just 20 days.

Hope it's helpful for you