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Three friends Anne, Bob and Chris work together to do a certain job. Time it takes them to do the work together to do a certain job. The it takes them to do the work together is 6 hours less than Anne would have take alone, 1 hour less than Bob would have taken alone and half the time Chris would have taken working alone text. How long did it take them to complete the job, working together ?

Correct Answer: 40 minutes
Let the time taken by the three friends together to do the work be x hours
Then, time taken by Anne alone = (x + 6) hours
Time taken by Bob alone = (x + 1) hours
Time taken by Bob alone = 2x hours
$$\therefore \frac{1}{{x + 6}} + \frac{1}{{x + 1}} + \frac{1}{{2x}} = \frac{1}{x}$$
$$ \Rightarrow $$ $$\frac{{2x\left( {x + 1} \right) + 2x\left( {x + 6} \right) + \left( {x + 1} \right)\left( {x + 6} \right)}}{{2x\left( {x + 6} \right)\left( {x + 1} \right)}}$$         $$ = $$ $$\frac{1}{x}$$
$$\eqalign{ & \Rightarrow 5{x^2} + 21x + 6 = 2\left( {{x^2} + 7x + 6} \right) \cr & \Rightarrow 3{x^2} + 7x - 6 = 0 \cr & \Rightarrow \left( {x + 3} \right)\left( {3x - 2} \right) = 0 \cr & \Rightarrow x = \frac{2}{3}{\text{ }}\left \cr & \therefore {\text{Required times}} \cr & = \frac{2}{3}{\text{ hours}} \cr & = \left( {\frac{2}{3} \times 60} \right){\text{hours}} \cr & = 40{\text{ minutes}} \cr} $$

Simplify the value of $$\frac{{{\text{0}}{\text{.9}} \times {\text{0}}{\text{.9}} \times {\text{0}}{\text{.9 + 0}}{\text{.2}} \times {\text{0}}{\text{.2}} \times {\text{0}}{\text{.2 + 0}}{\text{.3}} \times {\text{0}}{\text{.3}} \times {\text{0}}{\text{.3}} - {\text{3}} \times 0.9 \times {\text{0}}{\text{.2}} \times {\text{0}}{\text{.3}}}}{{{\text{0}}{\text{.9}} \times {\text{0}}{\text{.9 + 0}}{\text{.2}} \times {\text{0}}{\text{.2 + 0}}{\text{.3}} \times {\text{0}}{\text{.3}} - 0.9 \times {\text{0}}{\text{.2}} - {\text{0}}{\text{.2}} \times {\text{0}}{\text{.3}} - 0.3 \times 0.9}} = ?$$

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