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The time to plant a rice field is inversely proportional to the number of people who are working. A large field can be planted by five workers in 24 days. In order to finish the planting sooner, the farmer plans to hire additional workers. How many workers are needed to finish the field in 15 days?​

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Quinzengo

INVERSE VARIATION

EQUATION:

[tex]t = \frac{k}{w} [/tex]

where k is the constant of variation, t is the number of time/days, and w is the number of workers.

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First, solve for the constant of variation k using the formula k=tw where we multiply the number of time by the number of workers.

[tex]24 = \frac{k}{5} [/tex]

[tex]k = (24)(5)[/tex]

[tex]k = 120[/tex]

Therefore, the constant of variation is 120.

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Then, find the number of workers if the number of days is 15 using the equation of variation t=120w where 120 is the constant of variation.

[tex]t = \frac{120}{w} [/tex]

[tex]15 = \frac{120}{w} [/tex]

[tex]15w = 120 [/tex]

[tex] \frac{15w}{15} = \frac{120}{15} [/tex]

[tex]w = 8 [/tex]

Final Answer:

8 workers are needed to finish the field in 15 days.

Learn more about inverse variation: https://brainly.ph/question/9494275 » https://brainly.ph/question/8924304

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