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If Jesus completes a job in 21 hours less time than Cassie and they can do the job together in 10 hours how long will it take each to complete the job alone

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Answer to a math question If Jesus completes a job in 21 hours less time than Cassie and they can do the job together in 10 hours how long will it take each to complete the job alone

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Hester

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116 Answers

\text{Given:}

t_J = t_C - 21

\frac{1}{t_J} + \frac{1}{t_C} = \frac{1}{10}

1. Substituting into combined work formula:

\frac{1}{t_C - 21} + \frac{1}{t_C} = \frac{1}{10}

2. Multiplying by

$ t_C(t_C - 21) $

t_C + (t_C - 21) = \frac{t_C^2 - 21t_C}{10}

3. Combining and simplifying:

2t_C - 21 = \frac{t_C^2 - 21t_C}{10}

20t_C - 210 = t_C^2 - 21t_C

4. Solving quadratic equation:

t_C^2 - 41t_C + 210 = 0

t_C = \frac{41 \pm 29}{2}

5. Finding

$ t_C $

t_C = 35 \, \text{(valid solution)} \qquad t_C = 6 \, \text{(invalid)}

\text{Therefore, the time it takes each to complete the job alone is:}

t_C = 35 \, \text{hours}

t_J = 14 \, \text{hours}

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If Jesus completes a job in 21 hours less time than Cassie and they can do the job together in 10 hours how long will it take each to complete the job alone

Answer to a math question If Jesus completes a job in 21 hours less time than Cassie and they can do the job together in 10 hours how long will it take each to complete the job alone

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