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Solve each problem carefully and write your computation or solution



B. Mark can clean his room in 40 minutes and his brother can clean the same room in 60 minutes. How long will it take for them to clean the room together? Ans. 24 minutes


C. Anna spends 5 hours in picking 10 kaings of papaya in the garden. Lorna can pick the same amount of papaya in 6 hours. How long will it take if they work together? Round your answer to the nearest hour. Ans. 3 hours ​

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Answer:

B.

[tex] \tt{} \frac{x}{40} + \frac{x}{60} = 1[/tex]

LCD is 120. Multiply all the terms by the LCD.

[tex] \tt{}120 \bigg( \frac{x}{40} + \frac{x}{60} = 1\bigg)[/tex]

[tex] \tt{} \frac{120x}{40} + \frac{120x}{60} = 120[/tex]

[tex] \tt{}3x + 2x = 120[/tex]

[tex] \tt{}5x = 120[/tex]

[tex] \tt{}x = \frac{120}{5} [/tex]

[tex] \huge\boxed{ \tt{}x = 24 \: minutes} [/tex]

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C.

[tex] \tt{} \frac{x}{5} + \frac{x}{6} = 1[/tex]

LCD is 30. Multiply all the terms by the LCD.

[tex] \tt{}30 \bigg( \frac{x}{5} + \frac{x}{6} = 1 \bigg)[/tex]

[tex] \tt{} \frac{30x}{5} + \frac{30x}{6} = 30[/tex]

[tex] \tt{}6x + 5x = 30[/tex]

[tex] \tt{}11x = 30[/tex]

[tex] \tt{}x = \frac{30}{11} [/tex]

[tex] \tt{}x = 2.72727272727[/tex]

[tex] \huge \boxed{ \tt{}x = 3 \: hours} \\ \\ \\ \\ [/tex]

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