Question

1. Gary can load the truck in 30 minutes. If his son Kevin helps him, it takes them 12 minutes.
How long will it take Kevin to finish alone?

Answer 1

$\huge{\blue{\bold{\underline{\underline{Answer :}}}}}$

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$\large{\green{\underline \bold{\tt{Given :-}}}}$

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• Gary can load the truck in 30 minutes

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• If his son Kevin helps him, it takes them 12 minutes to load the truck

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$\large{\red{\underline \bold{\tt{To \: Find :-}}}}$

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• Time required for kelvin to finish the work alone

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$\large{\orange{\underline{\tt{Solution :-}}}}$

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• Let kelvin alone can finish loading the truck in x minutes

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$\underline{\bold{\texttt{Gary's 1 minute work :}}}$

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➠ $\sf \dfrac { 1 } { 30 }$

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$\underline{\bold{\texttt{Kelvin's 1 minute work :}}}$

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➠ $\sf \dfrac { 1 } { x}$

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$\underline{\bold{\texttt{1 minute work of Gary \& Kelvin together :}}}$

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➠ $\sf \dfrac { 1 } { 30 } + \dfrac { 1 } { x }$

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$\underline{\bold{\texttt{12 minute work of Gary \& Kelvin together :}}}$

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➠ $\sf 12(\dfrac { 1 } { 30 } + \dfrac { 1 } { x })$

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Given that if Gary & Kelvin works together for 12 minutes they would finish the work

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So,

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➜ $\sf 12(\dfrac { 1 } { 30 } + \dfrac { 1 } { x }) = 1$

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➜ $\sf \cancel { 12} ( \dfrac { x + 30 } { \cancel { 30} x }) = 1$

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➜ $\sf 2( \dfrac { x + 30 } { 5x }) = 1$

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➜ 2(x + 30) = 5x

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➜ 2x + 60 = 5x

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➜ 3x = 60

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➜ $\sf x = \dfrac { 60 } { 3 }$

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➨ x = 20

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• Hence Kelvin alone can load the truck in 20 minutes

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Answer 2

$\huge{\blue{\bold{\underline{\underline{Solution :}}}}}$

$\:\:$

• Let kelvin alone can finish loading the truck in x minutes

$\:\:$

$\underline{\bold{\texttt{Gary's 1 minute work :}}}$

$\:\:$

➠ $\sf \dfrac { 1 } { 30 }$

$\:\:$

$\underline{\bold{\texttt{Kelvin's 1 minute work :}}}$

$\:\:$

➠ $\sf \dfrac { 1 } { x}$

$\:\:$

$\underline{\bold{\texttt{1 minute work of Gary \& Kelvin together :}}}$

$\:\:$

➠ $\sf \dfrac { 1 } { 30 } + \dfrac { 1 } { x }$

$\:\:$

$\underline{\bold{\texttt{12 minute work of Gary \& Kelvin together :}}}$

$\:\:$

➠ $\sf 12(\dfrac { 1 } { 30 } + \dfrac { 1 } { x })$

$\:\:$

• Given that if Gary & Kelvin works together for 12 minutes they would finish the work

$\:\:$

So,

$\:\:$

➜ $\sf 12(\dfrac { 1 } { 30 } + \dfrac { 1 } { x }) = 1$

$\:\:$

➜ $\sf \cancel { 12} ( \dfrac { x + 30 } { \cancel { 30} x }) = 1$

$\:\:$

➜ $\sf 2( \dfrac { x + 30 } { 5x }) = 1$

$\:\:$

➜ 2(x + 30) = 5x

$\:\:$

➜ 2x + 60 = 5x

$\:\:$

➜ 3x = 60

$\:\:$

➜ $\sf x = \dfrac { 60 } { 3 }$

$\:\:$

➨ x = 20

$\:\:$

• Hence Kelvin alone can load the truck in 20 minutes

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